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Quiz 5
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Q.1
The ratio of the volume of a hemisphere and a cylinder circumscribing this hemisphere and having a common base is :
1 : 2
2 : 3
3 : 4
4 : 5
Q.2
What length of solid cylinder 2 cm in diameter must be taken to cast into a hollow cylinder of external diameter 12 cm, 0.25 cm thick and 15 cm long ?
42.3215 cm
44.0123 cm
44.0625 cm
44.6023 cm
Q.3
If the height of a right circular cone is increased by 200% and the radius of the base is reduced by 50%, then the volume of the cone :
remains unaltered
decreases by 25%
increases by 25%
increases by 50%
Q.4
A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick. The thickness of the bottom is:
90 cm
1 dm
1 m
1.1 cm
Q.5
What is the total surface area of a right circular cone of height 14 cm and base radius 7 cm?
344.35 cm
^{2}
462 cm
^{2}
498.35 cm
^{2}
None of these
Q.6
If the volume and surface area of a sphere are numerically the same, then its radius is :
1 unit
2 units
3 units
4 units
Q.7
A copper wire of length 36 m and diameter 2 mm is melted to form a sphere. The radius of the sphere (in cm) is :
2.5 cm
3 cm
3.5 cm
4 cm
Q.8
A bucket is in the from of a frustum of a cone and holds 28.490 litres of water. The radii of the top and bottom are 28 cm and 21 cm respectively. Find the height of the bucket.
15 cm
20 cm
25 cm
30 cm
Q.9
A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is:
12 kg
60 kg
72 kg
96 kg
Q.10
50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m
^{3}
, then the rise in the water level in the tank will be:
20 cm
25 cm
35 cm
50 cm
Q.11
A large cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. What is the ratio of the total surface areas of the smaller cubes and the large cube?
2 : 1
3 : 2
25 : 18
27 : 20
Q.12
How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?
5600
6000
6400
7200
Q.13
The capacities of two hemispherical vessels are 6.4 litres and 21.6 litres. The areas of inner curved surfaces of the vessels will be in the ratio of :
$$\sqrt 2 $$ : $$\sqrt 3 $$
2 : 3
4 : 9
16 : 81
Q.14
The base of a pyramid is an equilateral triangle of side 1 m. If the height of the pyramid is 4 metres, then the volume is :
0.550 m
^{3}
0.577 m
^{3}
0.678 m
^{3}
0.750 m
^{3}
Q.15
The slant height of a right circular cone is 10 m and its height is 8 m. Find the area of its curved surface.
30π m
^{2}
40π m
^{2}
60π m
^{2}
80π m
^{2}
Q.16
A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:
49 m
^{2}
50 m
^{2}
53.5 m
^{2}
55 m
^{2}
Q.17
Each side of a cube is decreased by 25%. Find the ratio of the volume of the original cube and the resulting cube = ?
64 : 1
27 : 64
64 : 27
8 : 1
Q.18
A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m
^{3}
) is:
4830
5120
6420
8960
Q.19
In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:
75 cu. m
750 cu. m
7500 cu. m
75000 cu. m
Q.20
A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:
720 m
^{3}
900 m
^{3}
1200 m
^{3}
1800 m
^{3}
Q.21
66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be:
84 meters
90 meters
168 meters
336 meters
Q.22
A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weights 8 g/cm
^{3}
, then the weight of the pipe is:
3.6 kg
3.696 kg
36 kg
36.9 kg
Q.23
The volume of a right circular cone which is obtained from a wooden cube of edge 4.2 dm wasting minimum amount of wood is :
19404 dm
^{3}
194.04 dm
^{3}
19.404 dm
^{3}
1940.4 dm
^{3}
Q.24
What is the volume in cubic cm of a pyramid whose area of the base is 25 sq cm and height 9 cm ?
60 cm
^{3}
75 cm
^{3}
90 cm
^{3}
105 cm
^{3}
Q.25
A semicircular sheet of paper of diameter 28 cm is bent to cover the exterior surface of an open conical ice-cream cup. The depth of the ice-cream cup is :
8.12 cm
10.12 cm
12.12 cm
14.12 cm
Q.26
If the volume and curved surface area of a cylinder are 616 m
^{3}
and 352 m
^{2}
respectively, what is the total surface area of the cylinder (in m
^{2}
)
429$$\,{\text{sq}}{\text{.m}}$$
419$$\,{\text{sq}}{\text{.m}}$$
435$$\,{\text{sq}}{\text{.m}}$$
421$$\,{\text{sq}}{\text{.m}}$$
417$$\,{\text{sq}}{\text{.m}}$$
Q.27
If the height of a right circular cone is increased by 200% and the radius of the base is reduced by 50%, then the volume of the cone :
Remains unaltered
Decrease by 25%
Increase by 25%
Increase by 50%
Q.28
The ratio of the surface area of a sphere and the curved surface area of the cylinder circumscribing the sphere is :
1 : 1
1 : 2
2 : 1
2 : 3
Q.29
If the surface area of two spheres are in the ratio of 4 : 25, then the ratio of their volumes is :
4 : 25
25 : 4
125 : 8
8 : 125
Q.30
The diameter of the iron ball used for the shot-put game is 14 cm. It is melted and then a solid cylinder of height $$2\frac{1}{3}$$ cm is made. What will be the diameter of the base of the cylinder ?
14 cm
$$\frac{{14}}{3}$$ cm
28 cm
$$\frac{{28}}{3}$$ cm
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