If a sphere of radius r is divided into four identical parts, then the total surface area of the four parts is

• 4πr² square unit

• 2πr² square unit

• 8πr² square unit

• 6πr² square unit

A cylinder with base radius 8 cm and height 2cm is melted to form a cone of height 6 cm. The radius of the cone will be

• 6 cm

• 8 cm

• 4 cm

• 4 cm

The base of a right pyramid is a square side 10 cm. If the height of the pyramid is 12 cm, then its total surface area is

• 400 cm²

• 460 cm²

• 260 cm²

• 260 cm²

The numerical values of the volume and the area of the lateral surface of a right circular cone are equal. If the height of the cone be h and radius be r, the value of  is

If a hemisphere is melted and four spheres of equal volume are made, the radius of each sphere will be equal to

• th of the radius of the hemisphere

• radius of the hemisphere

•  of the radius of the hemisphere
•  of the radius of the hemisphere

The radii of two solid iron spheres are 1 cm and 6 cm respectively. A hollow sphere is made by melting the two spheres. If the external radius of the hollow sphere is 9 cm, then its thickness (in cm) is

• 2

• 1.5

• 0.5

• 0.5

77.

A right prism has a triangular base, whose sides are 13 cm, 20 cm and 21 cm. If the altitude of the prism is 9 cm, then its volume is

• 1314 cm³

• 1134 cm³

• 1413 cm³

• 1413 cm³

The portion of a ditch 48m long, 16.5m wide and 4 m deep that can be filled with stones and earth available during excavation of a tunnel, cylindrical in shape, of diameter 4 m and length 56 m is 

If 64 buckets of water are removed from a cubical shaped water tank completely filled with water,  of the tank remains filled with water. The length of each side of the tank is 1.2 m. Assuming that all buckets are of the same measure, then the volume (in litres) of water contained by each bucket is

• 12

• 16

• 15

• 15

A plane divides a right circular cone into two parts of equal volume. If the plane is parallel to the base, then the ratio, in which the height of the cone is divided, is

• 1 : ∛2

• 1 : √2

• 1 : ∛2 + 1

• 1 : ∛2 - 1