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question_answer1)
If volume and surface area of a sphere are numerically equal, find its radius.
A)
2 units done
clear
B)
3 units done
clear
C)
4 units done
clear
D)
5 units done
clear
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question_answer2)
The base radius of a cylinder is\[1\frac{2}{3}\]times its height. The cost of painting its C.S.A. at 2paise/\[c{{m}^{2}}\] is Rs. 92.40.What volume of the paint is required?
A)
\[80850\text{ }c{{m}^{3}}\] done
clear
B)
\[~80580\text{ }c{{m}^{3}}\] done
clear
C)
\[~80508\text{ }c{{m}^{3}}\] done
clear
D)
\[85800\text{ }c{{m}^{3}}\] done
clear
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question_answer3)
The total surface area of a cylinder of height 6.5 cm is 220 sq cm. Find its volume.
A)
\[~25.025\text{ }c{{m}^{3}}\] done
clear
B)
\[2.5025\text{ }c{{m}^{3}}\] done
clear
C)
\[2502.5\,c{{m}^{2}}\] done
clear
D)
\[~250.25\text{ }c{{m}^{3}}\] done
clear
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question_answer4)
The height of a cylinder is 15 cm. The curved surface area is 660 sq. cm. Find its radius, \[(Take\,\pi \,as\,\frac{22}{7})\]
A)
7 cm done
clear
B)
9 cm done
clear
C)
6 cm done
clear
D)
11 cm done
clear
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question_answer5)
A cylindrical vessel contains 49.896 litres of liquid. Cost of painting its C.S.A. at 2 paise/sq cm is Rs. 95.04.What is its total surface area?
A)
\[5724\text{ }c{{m}^{2}}\] done
clear
B)
\[~7524\text{ }c{{m}^{2}}\] done
clear
C)
\[~5742\text{ }c{{m}^{2}}\] done
clear
D)
\[7254\text{ }c{{m}^{2}}\] done
clear
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question_answer6)
What is the ratio of volumes of two cones with the same radii?
A)
\[{{h}_{1}}:{{h}_{2}}\] done
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B)
\[{{r}_{1}}:{{r}_{2}}\] done
clear
C)
\[{{s}_{1}}:{{s}_{2}}\] done
clear
D)
\[1:2\] done
clear
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question_answer7)
What is the length of the longest pole that can be put in a room of dimensions\[10\,m\times 10\,m\times 5\,m?\]
A)
15 m done
clear
B)
16 m done
clear
C)
10 m done
clear
D)
12 m done
clear
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question_answer8)
The cost of painting the T.S.A. of cone at \[5ps/c{{m}^{2}}\]is Rs. 35.20 Determine the volume of the cone if its slant height is 25 cm.
A)
\[1223\,c{{m}^{2}}\] done
clear
B)
\[~1232\,c{{m}^{2}}\] done
clear
C)
\[~1323\,c{{m}^{2}}\] done
clear
D)
\[1332\,c{{m}^{2}}\] done
clear
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question_answer9)
A vessel is conical in shape. If its volume is 33.264 litres and height is 72 cm, what is the cost of repairing its C.S.A. at ` 12/sq. m?
A)
Rs. 5.94 done
clear
B)
Rs. 6.94 done
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C)
Rs. 7.95 done
clear
D)
Rs. 7.59 done
clear
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question_answer10)
A joker's cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the areas of the sheet required to make 10 such caps.
A)
\[5000\text{ }c{{m}^{2~}}\] done
clear
B)
\[~6200\text{ }c{{m}^{2}}\] done
clear
C)
\[5500\text{ }c{{m}^{2}}\] done
clear
D)
\[6000\text{ }c{{m}^{2}}\] done
clear
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question_answer11)
A hemispherical bowl is made of steel of 0.25 cm thickness. The inner radius of the bowl is 5 cm. Find the volume of steel used.
A)
\[42.15c{{m}^{3}}\] done
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B)
\[41.52c{{m}^{3}}\] done
clear
C)
\[41.28\,c{{m}^{3}}\] done
clear
D)
\[45.21\text{ }c{{m}^{3}}\] done
clear
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question_answer12)
How many litres of water flows out through a pipe having an area of cross- section of \[56c{{m}^{2}}\]in one minute, if the speed of water in pipe is 30 cm/sec?
A)
9 litres done
clear
B)
15 litres done
clear
C)
30 litres done
clear
D)
3 litres done
clear
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question_answer13)
A cylindrical vessel of diameter 9 cm has some water in it. A cylindrical iron piece of diameter 6 cm and height 4.5 cm is dropped in it. After it was completely immersed, find the rise in the level of water.
A)
0.8 cm done
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B)
2 cm done
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C)
1 cm done
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D)
0.4 cm done
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question_answer14)
A well, 14m deep is 2 m in radius. Find the cost of cementing the inner curved surface at the rate of Rs. 2 per square metre.
A)
Rs. 242 done
clear
B)
Rs. 352 done
clear
C)
Rs. 464 done
clear
D)
Rs. 294 done
clear
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question_answer15)
The radius of a sphere is increased by P%. What is the increase in its surface area?
A)
P % done
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B)
\[{{P}^{2}}%\] done
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C)
\[\left( 2P+\frac{{{P}^{2}}}{100} \right)%\] done
clear
D)
\[\frac{{{P}^{2}}}{2}%\] done
clear
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question_answer16)
The diameter of two cones are equal. If their slant heights are in the ratio 5:4, find the ratio of their curved surface areas.
A)
2 : 3 done
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B)
4 : 5 done
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C)
5 : 4 done
clear
D)
3 : 2 done
clear
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question_answer17)
A semi-circular sheet of metal of diameter 28 cm is bent into an open conical cup. Find the capacity of the cup.
A)
\[622\text{ }c{{m}^{3}}\] done
clear
B)
\[504\,c{{m}^{3}}\] done
clear
C)
\[645\text{ }{{m}^{3}}\] done
clear
D)
\[592\,{{m}^{3}}\] done
clear
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question_answer18)
The diameter of a garden roller is 1.4 m and it is 2 m long. How much area will it cover in 5 revolutions? \[(Take\,\pi =\frac{22}{7}.)\]
A)
11 sq. m done
clear
B)
16 sq. m done
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C)
28 sq. m done
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D)
44 sq. m done
clear
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question_answer19)
The volumes of two spheres are in the ratio 64 :27. Find the difference of their surface areas, if the sum of their radii is 7 units.
A)
\[28\pi \,\text{sq}\text{.units}\] done
clear
B)
\[64\pi \,\text{sq}\text{.units}\] done
clear
C)
\[88\,\pi \,\text{sq}\text{.units}\] done
clear
D)
\[4\,\pi \,\text{sq}\text{.units}\] done
clear
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question_answer20)
Into a conical tent of radius 7 m and vertical height 4.5 m, how many full bags of rice can be emptied, if volume of each bag is\[1.5\text{ }{{m}^{3}}.\]
A)
120 bags done
clear
B)
144 bags done
clear
C)
154 bags done
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D)
172 bags done
clear
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question_answer21)
Find the largest volume (in\[c{{m}^{3}}\]) of a cube that can be enclosed in a sphere of diameter 2 cm.
A)
1 done
clear
B)
\[2\sqrt{2}\] done
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C)
\[\pi \] done
clear
D)
\[\frac{8}{3\sqrt{3}}\] done
clear
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question_answer22)
Find the curved surface of a right circular cone, whose slant height and the base radius are 25 cm and 7 cm respectively.
A)
\[420\text{ }c{{m}^{2}}\] done
clear
B)
\[550\text{ }c{{m}^{2}}\] done
clear
C)
\[~460\text{ }c{{m}^{2}}\] done
clear
D)
\[~580\text{ }c{{m}^{2}}\] done
clear
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question_answer23)
A right circular cylinder has a height of 21 cm and base radius of 5 cm. Find the curved surface area of the cylinder.
A)
\[230\,c{{m}^{2}}\] done
clear
B)
\[~660\text{ }c{{m}^{2}}\] done
clear
C)
\[~550\text{ }c{{m}^{2}}\] done
clear
D)
\[~450\text{ }c{{m}^{2}}\] done
clear
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question_answer24)
The area of the curved surface of a right circular cylinder is \[4400\text{ }c{{m}^{2}}\]and the circumference of its base is 110 cm. Find the height of the cylinder.
A)
30 cm done
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B)
10 cm done
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C)
20 cm done
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D)
40 cm done
clear
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question_answer25)
The circumference of the base of a 9 m high wooden solid cone is 44 m. Find the slant height of the cone.
A)
\[\sqrt{120}m\] done
clear
B)
\[\sqrt{130}m\] done
clear
C)
\[\sqrt{150}m\] done
clear
D)
\[7\sqrt{5}m\] done
clear
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question_answer26)
If \[{{A}_{1}}{{A}_{2}}\]and\[{{A}_{3}}\]denote the areas of three adjacent faces of a cuboid, find its volume.
A)
\[{{A}_{1}}{{A}_{2}}{{A}_{3}}\] done
clear
B)
\[2{{A}_{1}}{{A}_{2}}{{A}_{3}}\] done
clear
C)
\[\sqrt{{{A}_{1}}{{A}_{2}}{{A}_{3}}}\] done
clear
D)
\[\sqrt[3]{{{A}_{1}}{{A}_{2}}{{A}_{3}}}\] done
clear
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question_answer27)
If 5 men are in a room of dimensions 3 \[m\times 4m\times 10m,\]what is the amount of air available for each of them?
A)
\[~48\text{ }{{m}^{3}}\] done
clear
B)
\[36\text{ }{{m}^{3}}\] done
clear
C)
\[~24{{m}^{3}}\] done
clear
D)
\[120\,{{m}^{3}}\] done
clear
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question_answer28)
If\[l\]is the length of a diagonal of a cube of volume V, what is the relation between \[l\] and V?
A)
\[3V={{l}^{3}}\] done
clear
B)
\[\sqrt{3V}={{l}^{3}}\] done
clear
C)
\[3\sqrt{3}V=2{{l}^{3}}\] done
clear
D)
\[3\sqrt{3}V={{l}^{3}}\] done
clear
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question_answer29)
If each edge of a cube is increased by 50%, what is the percentage increase in its surface area?
A)
50% done
clear
B)
75% done
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C)
100% done
clear
D)
125% done
clear
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question_answer30)
A cylinder of radius 12 cm contains water to a depth of 20 cm. A spherical iron ball is dropped into the cylinder and thus the level of water is raised by 6.75 cm. Find the radius of the ball. \[(Take\,\pi =\frac{22}{7}).\]
A)
8 cm done
clear
B)
9 cm done
clear
C)
10 cm done
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D)
11 cm done
clear
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question_answer31)
Find the volume of a cube whose surface area is \[150\text{ }c{{m}^{2}}.\]
A)
\[25\sqrt{5}c{{m}^{3}}\] done
clear
B)
\[~64\,c{{m}^{3}}\] done
clear
C)
\[~125c{{m}^{3}}\] done
clear
D)
\[27c{{m}^{3}}\] done
clear
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question_answer32)
The curved surface area of a right circular cylinder of height 14 cm is \[88\,c{{m}^{2}}.\] Find the volume of the cylinder, \[\left( \text{Take}\,\pi =\frac{22}{7}. \right)\]
A)
\[~22\text{ }c{{m}^{3}}\] done
clear
B)
\[~44\text{ }c{{m}^{3}}\] done
clear
C)
\[~88\,c{{m}^{3}}\] done
clear
D)
\[11\text{ }c{{m}^{3}}\] done
clear
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question_answer33)
A spherical ball of diameter 21 cm, is melted and recasted into cubes, each of side 1 cm. Find the number of cubes thus formed. (Use\[\pi =22/7.\])
A)
2057 done
clear
B)
1962 done
clear
C)
4851 done
clear
D)
3272 done
clear
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question_answer34)
If the areas of the adjacent faces of a rectangular block are in the ratio 2:3:4 and its volume is\[9000\text{ }c{{m}^{3}},\] what is the length of the shortest edge?
A)
30 cm done
clear
B)
20 cm done
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C)
15 cm done
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D)
10 cm done
clear
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question_answer35)
If each edge of a cube, of volume, V, is doubled, find the volume of the new cube.
A)
2V done
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B)
4V done
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C)
6V done
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D)
8V done
clear
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question_answer36)
Two cubes of side 6 cm each are joined end to end. Find the surface area of the resultant cuboid.
A)
\[~200\text{ }c{{m}^{2}}\] done
clear
B)
\[420\text{ }c{{m}^{2}}\] done
clear
C)
\[~360\text{ }c{{m}^{2}}\] done
clear
D)
\[270\text{ }c{{m}^{2}}\] done
clear
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question_answer37)
If each edge of a cube of surface area S is doubled, what is the surface area of the new cube?
A)
2S done
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B)
4S done
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C)
6S done
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D)
8S done
clear
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question_answer38)
Find the cost of constructing a wall 8 m long, 4 m high and 20 cm thick at the rate of Rs. 25 per \[{{m}^{3}}.\]
A)
Rs. 16 done
clear
B)
Rs. 80 done
clear
C)
Rs. 160 done
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D)
Rs. 320 done
clear
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question_answer39)
The circumference of the base of 9 m high wooden solid cone is 44 m. Find its volume. \[(\pi =\frac{22}{7}.)\]
A)
\[235\text{ }{{m}^{3}}\] done
clear
B)
\[~456\text{ }{{m}^{3}}\] done
clear
C)
\[365\text{ }{{m}^{3}}\] done
clear
D)
\[~462\text{ }{{m}^{3}}\] done
clear
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question_answer40)
If 10 cubic metres of clay is uniformly spread on a land of area 10 ares, what is the rise in the level of the ground?
A)
1 cm done
clear
B)
10 cm done
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C)
100 cm done
clear
D)
1000 cm done
clear
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question_answer41)
Volume of a cuboid is \[12\text{ }c{{m}^{3}}.\] Find the volume (in\[c{{m}^{3}}\]) of the cuboid if its sides are double.
A)
24 done
clear
B)
48 done
clear
C)
72 done
clear
D)
96 done
clear
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question_answer42)
The largest sphere is carved out of a cube of side 7 cm. Find the volume of the sphere. (Take\[\pi =3.14.\].)
A)
\[152.74\,c{{m}^{3}}\] done
clear
B)
\[243.41\text{ }c{{m}^{3}}\] done
clear
C)
\[179.67c{{m}^{3}}\] done
clear
D)
\[~195.01\,c{{m}^{3}}\] done
clear
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question_answer43)
On a particular day, the rain fall recorded on a terrace 6 m long and 5 m broad is 15 cm. Find the quantity of water collected on the terrace.
A)
300 litres done
clear
B)
450 litres done
clear
C)
3000 litres done
clear
D)
4500 litres done
clear
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question_answer44)
The height of sand in a cylindrical box drops 3 inches when 1 cubic foot of sand is poured out. What is the diameter, in inches, of the cylinder?
A)
\[\frac{24}{\sqrt{\pi }}\] done
clear
B)
\[\frac{48}{\sqrt{\pi }}\] done
clear
C)
\[\frac{32}{\sqrt{\pi }}\] done
clear
D)
\[\frac{48}{\pi }\] done
clear
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question_answer45)
If the diameter of the base of a closed right circular cylinder is equal to its height h, find its total surface area.
A)
\[2\pi {{h}^{2}}\] done
clear
B)
\[\frac{3}{2}\pi {{h}^{2}}\] done
clear
C)
\[\frac{4}{3}\pi {{h}^{2}}\] done
clear
D)
\[\pi {{h}^{2}}\] done
clear
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question_answer46)
The radius of a wire is decreased to its one-third. If its volume remains the same, by how many times will its length increase?
A)
3 times done
clear
B)
6 times done
clear
C)
9 times done
clear
D)
27 times done
clear
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question_answer47)
If the lateral surface area of a cube is \[1600\text{ }c{{m}^{2}},\] what is its edge?
A)
15 cm done
clear
B)
18 cm done
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C)
20 cm done
clear
D)
25 cm done
clear
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question_answer48)
A cylinder and a cone have equal base radii and equal heights. If their curved surface areas are in the ratio 8: 5, what is the ratio of their radii to heights?
A)
8 : 5 done
clear
B)
4 : 3 done
clear
C)
3 : 4 done
clear
D)
5 : 8 done
clear
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question_answer49)
If a square card board piece of side 4 cm is rotated 360° about one of its sides, what is the volume of the solid so formed?
A)
\[64\pi \,c{{m}^{3}}\] done
clear
B)
\[16\pi \,c{{m}^{3}}\] done
clear
C)
\[32\pi \,c{{m}^{3}}\] done
clear
D)
\[128\pi \,c{{m}^{3}}\] done
clear
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question_answer50)
The radius of a cylinder is doubled and its height is halved. What is the change in its curved surface area?
A)
Halved done
clear
B)
Doubled done
clear
C)
Remains the same done
clear
D)
Becomes four times done
clear
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question_answer51)
A right circular cylindrical tunnel of diameter 2 m and length 40 m is to be constructed from a sheet of iron. What is the area of the iron sheet required in\[{{m}^{2}}\]?
A)
\[40\pi \] done
clear
B)
\[60\pi \] done
clear
C)
\[80\pi \] done
clear
D)
\[100\pi \] done
clear
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question_answer52)
A cube of edge 'k' is divided into 'n? equal cubes. Determine the edge of the new cube.
A)
\[\sqrt{n}k\] done
clear
B)
\[\frac{k}{\sqrt[3]{n}}\] done
clear
C)
\[\sqrt[3]{n}k\] done
clear
D)
\[\frac{\sqrt[3]{n}}{k}\] done
clear
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question_answer53)
Two similar spherical drops each of radius 'r' cm are combined to form a bigger drop. Find the radius of the bigger drop.
A)
\[\sqrt[3]{2r}cm\] done
clear
B)
\[\sqrt{2r}cm\] done
clear
C)
\[\frac{r}{\sqrt[3]{2}}cm\] done
clear
D)
\[\frac{3\sqrt{2}}{r}cm\] done
clear
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question_answer54)
What is the total surface area of a hollow hemisphere of external and internal radii R and r?
A)
\[\pi ({{R}^{2}}+3{{r}^{2}})\] done
clear
B)
\[\pi (3{{R}^{2}}+{{r}^{2}})\] done
clear
C)
\[\pi (3{{r}^{2}}+2{{R}^{2}})\] done
clear
D)
\[\pi (2{{r}^{2}}+3{{R}^{2}})\] done
clear
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question_answer55)
If the surface area of a cube increases by 1%, what is the percentage increase in its volume?
A)
0.5 % done
clear
B)
1 % done
clear
C)
1.5% done
clear
D)
2% done
clear
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question_answer56)
Find the ratio of volume of a cylinder to the volume of a cone to the volume of a hemisphere of the same radius and height.
A)
1 : 1 : 1 done
clear
B)
3 : 2 : 1 done
clear
C)
1 : 2 : 3 done
clear
D)
3 : 1 : 2 done
clear
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