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
radius of the hemisphere
C.
Let R be the radius of hemisphere and r be the radius of sphere
∴ Volume of hemisphere =
∴ Volume of sphere =
According to the question,
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
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