objective Ques (104 results)
SSC CGL Mains 20241)The height of a right circular cone is 63 cm and the area of its curved surface is five times the area of its base. What is the volume (in cm3) of the cone? (Use π = 22/7)
10914.75
SSC CGL Mains 20242)A toy is in the form of a cone mounted on a hemisphere. The radius of the hemisphere and that of the cone is 36 cm and height of the cone is 105 cm. The total surface area (in cm2) of the toy is:
6588 π
SSC CGL Mains 20243)Find the volume (in cm3, rounded off to 2 decimal places) of a right circular cone of diameter 12 cm and height 5 cm. [Use π = 22/7 ]
188.57
SSC CGL Mains 20244)If the diameter of the base of a cone is 56 cm and its curved surface area is 3080 cm2, then what will be its volume (in cm3)? (Use π = 22/7)
17248
SSC CGL 20225)A solid metallic sphere of radius 12 cm is melted and recast into a cone having diameter of the base as 12 cm. What is the height of the cone?
192 cm
SSC CGL 20226)A conical vessel, whose internal radius is 20 cm and height is 27 cm, is full of water. If this water is poured into a cylindrical vessel with internal radius 15 cm, what will be the height to which the water rises in it?
16 cm
, Avg: 00:40 , 100%✓ SSC CGL 20227)Area of the floor of a cubical room is 64 m2. The length of the longest rod that can be kept in the room is:
\(8\sqrt3\) m
SSC CGL 20228)The radii of the ends of a frustum of a cone 7 cm high are 5 cm and 3 cm. Find its volume correct to one decimal place. \((use \pi = \frac{{22}}{7} )\)
359.3 cm3
, Avg: 01:22 , 100%✓ SSC CGL 20229)The radius of a right circular cylinder is four times of its height. If the height of the cylinder is 14 cm, then what is the volume of cylinder?
137984 cm3
SSC CGL 202210)How many metres of 2-m-wide cloth will be required to make a conical tent with a diameter of the base as 14 m and slant height as 9 m? (ignore wastage)
99 m
SSC CGL 202211)If the numerical value of twice the curved surface area of a right circular cylinder is equal to the numerical value of its volume, then what is the numerical value of the radius of the base of the cylinder?
4
, Avg: 01:44 , 100%✓ SSC CGL 202212)If the diameter of a solid hemisphere is 12.6 cm, then its volume is \((take \pi=\frac{22}{7} ):\)
523.908
, Avg: 00:40 , 100%✓ SSC CGL 202213)What is the edge of a cube whose volume is equal to the sum of the volumes of the cubes of edge 6 cm, 8 cm and 10 cm?
12 cm
, Avg: 01:36 , 66%✓ SSC CGL 202214)A solid metallic sphere of radius 13 cm is melted and recast into a cone having diameter of the base as 13 cm. What is the height of the cone?
208 cm
, Avg: 02:18 , 100%✓ SSC CGL 202215)A copper sphere of diameter 18 cm is drawn into a wire of diameter 6 mm. Find the length of the wire.
108 m
, Avg: 00:50 , 75%✓ SSC CGL 202216)A hemisphere of lead of radius 4 cm is cast into a right circular cone of height 72 cm. What is the radius of the base of the cone?
1.33 cm
, Avg: 00:49 , 83%✓ SSC CGL 202217)A solid cone of radius 7 cm and height 7 cm was melted along with two solid spheres of radius 7 cm each to form a solid cylinder of radius 7 cm. What is the curved surface area (in cm2) of the cylinder?
(Use \(π = \frac{22}{7}\) )
924
, Avg: 01:20 , 100%✓ SSC CGL 202218)What is the sum of the numbers between 400 and 500 such that when they are divided by 6, 12 and 16, it leaves no remainder?
912
, Avg: 00:34 , 100%✓ SSC CGL 202219)The length of the body diagonal of a cube is \(8 \sqrt{3}\) cm. What is the volume (in cm3) of the cube?
512
SSC CGL 202220)The total surface area of a right pyramid, with base as a square of side 8 cm, is 208 cm2. What is the slant height (in cm) of the pyramid?
9
, Avg: 01:15 , 75%✓ SSC CGL 202221)The length of a wire (in cm) of 0.1 mm radius that can be drawn from melting a solid copper sphere of diameter 6 cm is:
360000
, Avg: 00:37 , 12%✓ SSC CGL 202222)Two similar cuboid-shaped jugs have heights of 8 cm and 12 cm, respectively. If the capacity of the smaller jug is 80 cm3, what is the capacity of the bigger jug (in cm3)?
270
, Avg: 01:54 , 50%✓ SSC CGL 202223)From the body of a solid cube of edge 7 cm, a solid sphere is removed. The volume of the remaining solid was found to be \(163 {1 \over 3}\) cm3. What is the diameter (in cm) of the sphere? (Take π = 22/7 )
7
, Avg: 00:47 , 83%✓ SSC CGL 202224)If the volume of a sphere is 4,851 cm3, then what is this diameter (in cm)? (Take π = 22/7 )
21
, Avg: 01:24 , 80%✓ SSC CGL 202225)A river 6 m deep and 35 m wide is flowing at the rate of 2.5 km/h, the amount of water that runs into the sea per minute is:
8750 m3
, Avg: 02:19 , 66%✓ SSC CGL 202226)The circumference of the base of a right circular cylinder is 62.8 cm and its volume is 8792 cm2 . What is the curved surface ( in cm2 ) of the cylinder? (Take π = 3.14 )
1758.4
SSC CGL 202227)A hemispherical depression of diameter 4 cm is cut out from each face of a cubical block of sides 10 cm. Find the surface area of the remaining solid (in cm2). (Use \(\pi = \frac{22}{7} \))
675\(\frac{3}{7}\)
, Avg: 00:49 , 100%✓ SSC CGL 202228)Let x cm2 be the surface area and y cm3 be the volume of a sphere such that y = 14x. What is the radius (in cm) of the sphere?
42
, Avg: 01:59 , 50%✓ SSC CGL 202229)The curved surface area of a right circular cylinder is 616 cm2 and the area of its base is 38.5 cm2. What is the volume (in cm3) of the cylinder? (Take \(\pi = \frac{22}{7}\) )
1078
, Avg: 01:10 , 57%✓ SSC CGL 202230)A cylindrical vessel of diameter 32 cm is partially filled with water. A solid metallic sphere of radius 12 cm is dropped into it. What will be the increase in the level of water in the vessel (in cm)?
9
, Avg: 01:46 , 90%✓ SSC CGL 202231)How many small solid spheres each of 5 mm radius can be made out of a metallic solid cone whose base has radius 21 cm and height 30 cm?
26460
, Avg: 00:35 , 90%✓ SSC CGL 202232)If the volume of a sphere is equal to that of a cylinder having the same radius, then find the ratio of the radius to the height of the cylinder.
3 ∶ 4
, Avg: 00:59 , 69%✓ SSC CGL 202233)What is the difference in the volume (in cm3) of a sphere of radius 7 cm and that of a cone of radius 7 cm and height 10 cm? (Use π = 22/7 )
924
, Avg: 00:33 , 50%✓ SSC CGL 202234)A 35 cm high bucket in the form of a frustum is full of water. Radii of its lower and upper ends are 12 cm and 18 cm, respectively. If water from this bucket is poured in a cylindrical drum, whose base radius is 20 cm, then what will be the height of water (in cm) in the drum?
19.95
, Avg: 00:44 , 76%✓ SSC CGL 202235)A solid cube of side 8 cm is dropped into a rectangular container of length 16 cm, breadth 8 cm and height 15 cm which is partly filled with water. If the cube is completely submerged, then the rise of water level (in cm) is:
4
SSC CPO 202036)Let A and B be two cylinders such that the capacity of A is the same as the capacity of B. The ratio of the diameters of A and B is 1 ∶ 4. What is the ratio of the heights of A and B?
16 : 1
, Avg: 00:04 , 100%✓ SSC CPO 202037)If the volume of a sphere is 4851 cm3, then its surface area (in cm2) is: (Taken \(\pi={22\over 7}\))
1386
, Avg: 00:30 , 50%✓ SSC CPO 202038)The ratio of the total surface area and volume of a sphere is 2 ∶ 7. Its radius is:
10.5 cm
, Avg: 01:51 , 100%✓ SSC CPO 202039)The radius of the base of a cylinder of a cylinder is 14 cm and its volume is 6160 cm3. The curved surface area (in cm2) is:
(take π = 22/7)
880
, Avg: 02:55 , 100%✓ SSC CPO 202040)A solid metallic cube of side 9 cm and a solid metallic cuboid having dimensions 5 cm, 13 cm, 31 cm are melted to from a single cube. How much (in Rs.) is the cost to polish the new cube at a rate of Rs. 10 per cm2?
11,760
, Avg: 01:14 , 100%✓ SSC CPO 202041)A solid sphere of radius 11 cm is melted and recast into small solid spheres of radius 2 cm each. How many maximum number (in integer) of such spheres can be made?
166
, Avg: 01:28 , 100%✓ SSC CPO 202042)A 9 cm solid metallic cube and a solid metallic cuboid having dimensions 5 cm, 13 cm, 31 cm are melted and recast into a single cube. What is the total surface area (in cm2) of the new cube?
1176
, Avg: 00:41 , 60%✓ SSC CPO 202043)The radius of the base of a cylinder is 14 cm and its curved surface area is 880 cm2. Its volume (in cm3) is:
6160
SSC Selection Post Matric 202244)The circumference of a circular field is 704 m. What is the cost of levelling it at Rs. 15.25/ m2 ? (take \(\pi = \frac{22}{7}\))
Rs. 6,01,216
, Avg: 00:58 , 78%✓ SSC CHSL 202145)The square of the diagonal of a cube is 2175 cm2. What is the total surface area (in cm2) of the cube?
4350
, Avg: 00:36 , 100%✓ SSC CHSL 202146)A solid metallic sphere of radius 12 cm is melted and recast in the form of small spheres of radius 2 cm. How many small spheres are formed?
216
, Avg: 02:19 , 80%✓ SSC CHSL 202147)If the volume of a sphere is \(697 \frac{4}{21}\) cm3, then its radius is: (Take π = 22/7)
5.5 cm
, Avg: 01:47 , 50%✓ SSC CHSL 202148)How many bricks each measuring 64 cm × 11.25 cm × 6 cm, will be needed to build a wall measuring 8 m × 3 m × 22.5 m?
125000
, Avg: 01:44 , 100%✓ SSC CHSL 202149)The volume of a right circular cone is 462 cm3. If its height is 12 cm, then the area of its base (in cm2) is:
115.5
, Avg: 00:29 , 87%✓ SSC CHSL 202150)A solid metallic sphere of radius 10 cm is melted and recast into spheres of radius 2 cm each. How many such spheres can be made?
125
SSC CHSL 202151)The total surface area of a solid cube is 4.86 m2. It is melted and recast into a right circular cylinder of radius 0.3 m. What is the height (in m) of the cylinder (correct to one decimal place)? Take \(\pi = \frac{22}{7}\) .
2.6
, Avg: 02:32 , 100%✓ SSC CHSL 202152)A solid cube having volume 46656 cm3 is cut into 27 cubes of equal volume. The surface area (in cm2) of the smaller cubes is:
864
, Avg: 01:18 , 50%✓ SSC CHSL 202153)How many spherical bullets, each bullet being 7 cm in diameter, can be made out of a cube of lead whose edge measures 77 cm? (Take π = 22/7)
2541
, Avg: 00:50 , 66%✓ SSC CHSL 202154)From a rectangular sheet of dimensions 32 cm × 18 cm, a square of side 3 cm is cut from the four corners of the sheet and a box is made. The volume of the box is:
936 cm3
, Avg: 01:11 , 100%✓ SSC CHSL 202155)The radius of a sphere is 9 cm. It is melted and drawn into a wire of radius 0.3 cm. The length of the wire is:
108 m
, Avg: 00:52 , 66%✓ SSC CHSL 202156)The volume of a metallic cylindrical pipe is 3564 cm3. If its external radius is 12 cm and thickness is 3 cm, then the length of the pipe will be: (take π = 22/7)
18 cm
, Avg: 01:14 , 25%✓ SSC CHSL 202157)A solid metallic hemisphere of radius 6.3 cm is melted and recast into a right circular cylinder of radius 9 cm. What is the height (in cm, correct to one decimal place) of the cylinder?
2.1
, Avg: 01:42 , 100%✓ SSC CHSL 202158)if the diameter of the base of a cone is 18 cm and its curved surface area is \(424\frac{2}{7} \)cm2, then its height will be: (Take π = 22/7)
12 cm
, Avg: 02:59 , 50%✓ SSC CHSL 202159)A solid metallic cube of side 4.4 cm is melted and recast in the form of a wire of radius 2 mm. Find the length (in cm) of the wire. (Use π = 22/7)
677.6
, Avg: 01:31 , 100%✓ SSC CHSL 202160)A solid metallic right circular cylinder has diameter 32 cm and height 9 cm. It is melted and recast into a solid sphere. What is the radius (in cm) of the sphere?
12
, Avg: 02:00 , 100%✓ SSC CHSL 202161)The three medians RQ, SP, and TN of ΔRST intersect at point O. If the area of \(\triangle RST\) is 48 cm2, then the area of the quadrilateral SQON is:
16 cm2
, Avg: 00:33 , 100%✓ SSC CHSL 202162)What is the length (in cm) of the longest rod that can be fitted in a box dimensions 28 cm × 4 cm × 10 cm ?
30
, Avg: 00:35 , 75%✓ SSC CHSL 202163)If the ratio of the curved surface area and volume of a right circular cylinder is 5 ∶ 7, then its radius is:
2.8 unit
, Avg: 01:09 , 29%✓ SSC CHSL 202164)A solid metallic cube of side 20cm is melted and recast into a cuboid of length 40 cm and breadth 40 cm. What is the length (in cm) of the body diagonal of the cuboid?
\(5\sqrt {129}\)
, Avg: 01:01 , 80%✓ SSC CHSL 202165)The sum of the radius of the base and the height of a closed solid cylinder is 12.5 cm. If the total surface area of the cylinder is 275 cm2, then its radius is: \(\rm \left(Take \space\pi = \frac{22}{7}\right)\)
3.5 cm
, Avg: 00:19 , 100%✓ SSC CHSL 202166)The length of a rectangle is five times of its breadth. If the area of the rectangle is 3125 cm2, then what is the length of the rectagle?
125 cm
, Avg: 01:29 , 75%✓ SSC CGL 202067)If the radius of a right circular cylinder is decreased by 10%, and the heightis increased by 20%, then the percentage increase/decrease in its volume is :
decrease by 2.8%
Volume of right circular cylinder =\( \pi r^2h\);
Radius of a right circular cylinder is decreased by 10%, and the height is increased by 20% so,
r1 =\( r \times 90/100 = 0.9r\) ;
h1 = \(h \times 120/100 = 1.2h\) ;
Volume of new right circular cylinder =\(\pi r1^2h1 = \pi (0.9r)^2(1.2h) = 0.972(\pi r^2h)\) ;
Decrements in volume =\( \pi r^2h - 0.972(\pi r^2h) = 0.028(\pi r^2h)\) ;
Percentage Decrements in volume = \(\frac{0.028(\pi r^2h)}{(\pi r^2h)} \times 100\) = 2.8%
SSC CGL 201668)A cylinderical container of 32 cm height and 18 cm radius is filled with sand. Now all this sand is used to form a conical heap of sand. If the height of the conical heap is 24 cm, what is the radius of its base?
36 cm
, Avg: 00:40 , 100%✓ SSC CGL 202069)Find the height of a cuboid whose volume is 330 \(cm^3\) and base area is 15 \(cm^2\) .
22 cm
Volume of cuboid = Base area x height
330 = 15 x height
Height = 330/15 = 22 cm
, Avg: 00:51 , 80%✓ SSC CGL 202070)The volumes of spheres A and B are in the ratio 125 : 64. If the sum of radii of A and B is 36 cm,then the surface area (in \(cm^2\)) of A is:
\(1600\pi\)
Let, radius of sphereA = R cm; Radus of sphere B = r cm; so \({{4\over3}\pi{R}^3}\over{{4\over3}\pi{r}^3}\) = \(125\over64\);
\({R^3\over r^3 }=({5\over4})^3\) ; \({R\over r} = {5\over4} = 5: 4\); and R + r = 36 cm; R = \({5\over9}\times36 = 20 cm\);
Surface area of sphere A = \(4\pi{R}^2= 4\pi\times(20)^2=1600\pi {cm}^2\)
, Avg: 00:57 , 100%✓ SSC CGL 201971)If the volume of a sphere is 4851 \(cm^3\), then its surface area (in \(cm^2\)) is: (Take \(\pi={22\over7}\))
1386
\(V = {4\over 3} \pi r^3 = \) 4851 ;
r = \({21\over 2} cm\) ;
S.A = \(4 \pi r^2\) = 1386 sqcm
SSC CGL 201972)If the curved surface area of a solid cylinder is one-third of its total surface area, then what is the ratio of its diameter to its height?
4 : 1
SSC CGL 201973)A solid cube is cut into three cuboids of same volumes. What is the ratio of the surface area of the cube to the sum of the surface areas of any two of the cuboids so formed?
9 : 10
, Avg: 01:20 , 50%✓ SSC CGL 201974)A hemispherical bowl of internal diameter 36 cm is full of a liquid. This liquid is to be filled into cylindrical bottles each of radius 3 cm and height 12 cm. How many such bottles are required to empty the bowl?
36
, Avg: 01:39 , 100%✓ SSC CGL 201975)A right circular solid cone of radius 3.2 cm and height 7.2 cm is melted and recast into a right circular cylinder of height 9.6 cm. What is the diameter of the base of the cylinder?
3.2 cm.
, Avg: 00:58 , 75%✓ SSC CGL 201976)If the diameter of the base of a right circular cylinder is reduced by \(33\frac{1}{3}\)% and its height is doubled, then the volume of the cylinder will :
decrease by \(11\frac{1}{9}\)%
, Avg: 00:50 , 41%✓ SSC CGL 201977)The base of a right pyramid is an equilateral triangle with side 8 cm, and the height of the pyramid is \(24\sqrt3\) cm. The volume (in \(cm^3\)) of the pyramid is:
384
Volume of pyramid = (1/3) × Area of base × height
The base of a right pyramid is an equilateral triangle with side 8 cm, and the height of the pyramid is 24√3 cm.
Volume = (1/3) × (√3/4) × 82 × 24√3
⇒ 384 cm3
, Avg: 01:47 , 100%✓ SSC CGL 201978)A solid metallic sphere of radius 8 cm is melted and drawn into a wire of uniform cross-section. If the length of the wire is 24 m, then its radius (in mm) is:
\(5\frac{1}{3}\)
, Avg: 00:57 , 80%✓ SSC CGL 201979)A cylindrical vessel of radius 3.5 m is full of water. If 15400 litres of water is taken out from it, then the drop in the water level in the vessel will be:
40 cm
, Avg: 01:19 , 100%✓ SSC CGL 201980)The base of a right prism is a triangle with sides 20 cm, 21 cm and 29 cm. If its volume is 7560 \(cm^3\), then its lateral surface area (in \(cm^2\)) is:
2520
, Avg: 00:39 , 75%✓ SSC CGL 201981)The area of the base of a right circular cone is \(400\pi\) and its height is 15 cm. The curved surface area of the cone (in \(cm^2\)) is:
\(500\pi\)
, Avg: 04:28 , 33%✓ SSC CGL 201982)A sector of radius 10.5 cm with the central angle \(120^0\) is folded to form a cone by joining the two bounding radii of the sector. What is the volume (in \(cm^3\)) of the cone so formed?
\({343\sqrt2\over12}\pi\)
Radius of sector r = 10.5 cm
Circumference of sector whose angle is 120° = 2 πr × (θ/360) = 2 × (22/7) × 10.5 × (120/360) = 22cm
If we make cone from sector then,
Slant height (l) of the cone = radius of sector = 10.5 cm
Circumference of the cone = 22
2πr = 22, where r is the radius of cone
⇒ 2 × (22/7) × r = 22
⇒ r = 7/2 = 3.5 cm
As we know,
⇒ l2 = r2 + h2
⇒ (10.5)2 = (3.5)2 + h2
⇒ h2 = 110.25 – 12.25
⇒ h = 7 √2 cm
Volume of the cone = (1/3) × πr2h = (1/3) × π × (7/2) × (7/2) × 7 √2
SSC CGL 201983)The internal diameter of a hollow hemispherical vessel is 24 cm. It is made of a steel sheet which is 0.5 cm thick, What is the total surface area (in \(cm^2\)) of the vessel?
\(612.75\pi\)
, Avg: 02:38 , 50%✓ SSC CGL 201984)A solid cylinder of base radius 12 cm and height 15 cm is melted and recast into n toys each in the shape of a right circular cone of height 9 cm mounted on a hemisphere of radius 3 cm. The value of n is:
48
, Avg: 00:58 , 50%✓ SSC CGL 201985)The radius of the base of a right circular cylinder is 3 cm and its curved surface area is 60\(\pi cm^2\) , The volume of the cylinder (in \(cm^3\)) is:
\(90\pi\)
, Avg: 00:42 , 80%✓ SSC CGL 201986)A tank is in the form of a cuboid with length 12 m. If 18 kilolitre of water is removed from it, the water level goes down by 30cm. What is the width (in m) of the tank?
5
Let the length of the tank = 12 m
Height of the tank = 30 cm = 30/100 m = 0.3 m
Let the width of the tank be w m
According to the question
12 × b × 0.3 = 18
b = 5m
, Avg: 01:15 , 71%✓ SSC CGL 201987)A 15 metre deep well with radius 2.8 metre is dug and the earth taken out from it is spread evenly to form a platform of breadth 8 metre and height 1.5 metre. What will be the length of the platform? (Take \(\pi={22\over7}\))
30.8 metre
Height of the well H = 15 m and radius of the well r = 2.8 m
Let the length of the platform be l m
Breadth of the platform b = 8 m
Height of the platform h = 1.5 m
According to the question
lbh = πr2h
l × 8 × 1.5 = (22/7) × 2.8 × 2.8 × 15
⇒ l = 30.8 m
Length of the platform is 30.8 m
, Avg: 00:25 , 100%✓ SSC CGL 201988)A right prism has height 18 cm and its base is a triangle with sides 5 cm, 8 cm and 12 cm. What is its lateral surface area (in \(cm^2\)) ?
450
, Avg: 02:25 , 25%✓ SSC CGL 201989)A sphere of maximum volume is cut out from a solid hemisphere. What is the ratio of the volume of the sphere to that of the remaining solid?
1 : 3
, Avg: 06:11 , 100%✓ SSC CGL 201990)The base of a right pyramid is an equilateral triangle with area \(16\sqrt3cm^2\) . If the area of one of its lateral facesis 30 \(cm^2\) , then its height (in cm.) is :
\(\sqrt{611\over12}\)
, Avg: 05:51 , 75%✓ SSC CGL 201991)The radius and the height of a right circular cone are in the ratio 5 : 12. Its curved surface area is 816.4\(cm^2\) , What is the volume (in \(cm^3\)) of the cone? (Take \(\pi =3.14\))
2512
, Avg: 02:55 , 60%✓ SSC CGL 201992)The radius of the base of a right circular cylinder is increased by 20%. By what percent should its height be reduced so that its volume remains the same as before?
\(30\frac{5}{9}\)
Let the height be reduced by x%. r1 = 1.2r; h1 = \({(100-x)h\over100}\); \(\pi r^2h=\pi(1.2r)^2\times{(100-x)h\over100}\); \(x={44\over1.44}={30\frac{5}{9}}\)
, Avg: 01:16 , 66%✓ SSC CGL 201993)N solid metallic spherical balls are melted and recast into a cylindrical rod whose radius is 3 times that of a spherical ball and height is 4 times the radius of a spherical ball. The value of N is:
27
N volume of solid metallic spherical balls = volume of cylindrica; \(N {\times4\over3}\pi{r}^3= \pi(3r)^2\times4r\);
=\(N {\times4\over3}\pi{r}^3= 36\pi{r}^3\);
N= 27
, Avg: 00:36 , 75%✓ SSC CGL 201994)The volume of a right pyramid is \( 45\sqrt{3} cm^3\) and its base is an equilateral triangle with side 6 cm. What is the height(in cm)of the pyramid?
15
Side of equilateral triangle = 6 cm;
Area of equilateral triangle =\( \frac{\sqrt{3}}{4}a^2 = \frac{\sqrt{3}}{4}6^2 = 9\sqrt 3\);
The volume of a right pyramid = \(45\sqrt{3} cm^3; \frac{1}{3}9\sqrt 3h = 45\sqrt{3} cm^3;\)
h = 15 cm
SSC CGL 201995)If the radius of a sphere is increased by 4 cm, its surface area is increased by \(464 \pi cm^2\) . What is the volume(in \(cm^3\)) of the original sphere?
\(\frac{15625}{6}\pi\)
Difference in the surface area =\( 464 \pi;\)
\(4\pi(r + 4)^2 - 4\pi r^2 = 464 \pi;\)
\(4\pi[r^2 + 16 + 8r - r^2] = 464 \pi;\)
16 + 8r = 116;
r = 100/8 = 25/2 cm;
Volume of the the sphere =\( \frac{4}{3} \pi r^3 = \frac{4}{3} \pi (25/2)^3 = \frac{15625}{6} \pi\)
, Avg: 00:53 , 25%✓ SSC CGL 201996)Three solid metallic spheres whose radii are 1 cm, X cm and 8 cm, are melted and recast into a single solid sphere of diameter 18 cm. The surface area (in \(cm^2\)) of the sphere with radius x cm is:
\(144 \pi\)
Volume of solid sphere =\( \frac{4}{3} \pi r^3\);
Radius of single solid sphere = 18//2 = 9 cm;
Volume of single solid sphere = Volume of three solid metallic spheres;
\(\frac{4}{3} \pi (9)^3 = \frac{4}{3} \pi[1^3 + x^3 + 8^3];\)
729 = 512 + 1 + \(x^3\);
\(x^3\)= 216;
x = 6 cm;
Surface area = \(4\pi r^2 = 4\pi 6^2 = 144 \pi\)
, Avg: 01:42 , 33%✓ SSC CGL 201997)The internal and external radii of a hollow hemispherical vessel are 6 cm and 7 cm respectively. What is the total surface area (in \(cm^2\)) of the vessel?
\(183 \pi\)
Total surface area of the vessel = External surface area + internal surface area + upper portion area
r1 = 6 cm;
r2 = 7 cm;
= \(2 \pi (r2)^2 + 2 \pi (r1)^2 + \pi ((r2)^2 - (r1)^2)
= \pi[2 \times 7^2 + 2 \times 6^2 + (r2)^2 - (r1)^2]
= \pi[98 + 72 + 49 - 36] = 183\pi\)
, Avg: 00:49 , 50%✓ SSC CGL 201998)The lateral surface area of a cylinder is \(352 cm^2\). If its height is 7 cm, then its volume(in \(cm^3\)) is: (Take\( \pi = \frac{22}{7}\))
1408
The lateral surface area of a cylinder =\( 352 cm^2.\)
\(2\pi r h \)= 352
\(2\pi r \times 7\)= 352
r = \(\frac{176}{7\times 22/7} \)= 8
Volume = \(\pi r^2 \times h\) = \(\frac{22}{7} \times(8)^2 \times 7\)
= \(1408 cm^3\)
, Avg: 00:57 , 60%✓ SSC CGL 201999)The base of right prism is a trapezium whose parallel sides are 11 cm and 15 cm and the distance between them is 9 cm. If the volume of the prism is 1731.6\( cm^3,\) then the height(in cm) of the prism will be:
14.8
Volume = area of base \times height ;
Base area =\( \frac{1}{2} \times (l_1 + l_2) \times\) h =\( \frac{1}{2} \times (11 +15) \times 9\) = 117 \(cm^2\)
Height =\( \frac{volume}{base area}\) = \(\frac{1731.6}{117}\) = 14.8 cm
, Avg: 01:38 , 33%✓ SSC CGL 2019100)If a cuboid of dimensions 32 cm x 12 cm x 9 cm is cut into two cubes of same size, what will be the ratio of the surface area of the cuboid to the total surface area of the two cubes?
65 : 72
For big cuboid,
l = 32 cm, b = 12 cm, h = 9 cm;
Surface area = \(2(l \times b + b \times h + h \times l)\)
= \(2(32 \times 12 +12 \times 9 + 9 \times 32)\) = 2(384 + 108 + 288) = 1560
Assume that cuboid is melted to same size of cube so,
\(l \times b \times h = 2 \times a^3;\)
\(32 \times 12 \times 9 = 2 \times a^3;\)
\(1728 = a^3;\)
a = 12 cm;
Surface area of cube =\( 6 \times 12^2 \)= 864;
Ratio of the surface area of the cuboid to the total surface area of the two cubes = \(1560 : 2 \times 864 \)= 65 : 72
, Avg: 01:29 , 50%✓ SSC CGL 2019101)If the diameter of the base of a cone is 42 cm and its curved surface area is 2310 \({cm}^2\), then what will be its volume (in \({cm}^3\))?
12936
Diameter of the base of a cone = 42 cm;
radius(r) = 42/2 = 21 cm;
Curved surface area =\( 2310 cm^2;\)
\(\pi r l \)= 2310;
\(\frac{22}{7}\times 21 \times l \)= 2310;
l = 35;
\(l^2 = r^2 + h^2;\)
\(35^2 = 21^2 + h^2;\)
\(h^2 = 1225 - 441 = 784;\)
h = 28 cm;
Volume = \(\frac{1}{3} \pi r^2 h = \frac{1}{3} \times \frac{22}{7} 21^2 \times 28
= 12936 cm^3\)
, Avg: 00:54 , 80%✓ SSC CGL 2019102)If the radius of the base of a cone is doubled, and the volume of the new cone is three times the volume of the original cone, then what will be the ratio of the height of the original cone to that of the new cone?
4 : 3
Volume of the cone =\( \frac{1}{3} \times \pi r^2 h;\)
\(\frac{v_1}{v_2} = \frac{(r_1)^2(h_1)}{(r_2)^2(h_2)};\)
\(\frac{h_1}{h_2} = \frac{(r_1)^2(v_2)}{(r_2)^2(v_1)};\)
\(\frac{h_1}{h_2} = \frac{(2r_1)^2(v_2)}{(r_2)^2(3v_2)};\)
\(h_1 : h_2 = 4 : 3\)
, Avg: 00:56 , 42%✓ SSC CGL 2019103)A right circular cylinder of maximum volume is cut out from a solid wooden cube.The material left is what percent of the volume (nearest to an integer) of the original cube?
21
Side of cube = a;
Volume of cube =\( a^3;\)
For the maximum volume,
Height of right circular cylinder = a;
Diameter = a;
Radius =\( a/2;\)
Volume of right circular cylinder = \(\pi r^2 h = \frac{22}{7} \times (\frac{a}{2})^2 \times a = \frac{11}{14}a^3 =0.78a^3;\)
Material left = \(a^3 - 0.7857a^3 = 0.2143a^3;\)
Percentage material left = \(\frac{0.2143a^3}{a^3} \times 100 = 21.43 \approx 21%\)
, Avg: 04:22 , 80%✓ SSC CGL 2020104)The length, breadth and height of a cuboidal box are in the ratio 7 : 5 : 3 and its whole surface area is 27832 sq cm. Its volume is :
A)208120 \(cm^3\)
B)280120
\(cm^3\)
C)288100 \(cm^3\)
D)288120
288120 \(cm^3\)
l = 7 k cm, b = 5 k cm. h = 3 k cm. TSA = 27832sq.cm. ⇒2 (lb + bh + hl) = 27832 ⇒ k = 14
l = 98cm, b= 70cm, h = 42cm
volume of cuboidal box =( 98 x 70 x 42) cu. cm = 288120 cu cm