# Aptitude Volume and Surface Area Test Paper 3

11) If the curved surface area of a sphere is same as the curved surface area of a hemisphere, find the radius of the hemisphere.

1. Same as that of the sphere.
2. times that of the sphere.
3. times that of the sphere.
4. 2 times that of the sphere.

Explanation:

Curved surface area of a sphere = Curved surface area of a hemisphere
4 π R2= 2 π r2
2 R2= r2
Radius of hemisphere i.e. 'r' = = R

12) The radii of two cylinders are in the ratio of 2: 3 and their heights are in the ratio of 5: 3. The ratio of their volume is

1. 4: 9
2. 9: 4
3. 20: 27
4. 20: 25

Explanation:

Let the radius of both cylinders be 2x and 3x.
Let the height of both cylinders be 5y and 3y.
Ratio of the volume of two cylinders Ratio = 20: 27

13) The radius of road roller is 1 meter and length 7/22 meter. When it is rolled on a ground then it rolls 500 times to level the ground. But it was found that on 5% part of the ground, roller rolled twice. What is the total area of the ground?

1. 1000/Π2 m2
2. 975 m2
3. 975 m2
4. 950 m2

Explanation:

Let the area of the ground = x meter
The area covered in 1 revolution by the roller = 2Πrl 14) A copper sphere of radius 3 cm is beaten and drawn into a wire of diameter 0.2 cm. The length of the wire is

1. 9 m
2. 12 m
3. 18 m
4. 36 m

Explanation:

Radius of wire = = 0.1

Volume of sphere = Volume of cylinder 15) A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted to form a solid cylinder of base diameter 8 cm. What is the height of the cylinder?

1. 4.5 cm
2. 4.57 cm
3. 4.67 cm
4. 4.7 cm

Explanation:

Let the height of the cylinder be h.
According to question:
Volume of cylinder = Volume of hollow sphere Aptitude Volume and Surface Area Test Paper 1
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