The volume of a solid hemisphere is 29106 cm³. Another hemisphere whose volume is two-third of the above is carved out. Find the radius of the new hemisphere.

A cylindrical glass with diameter 20 cm has water to a height of 9 cm. A small cylindrical metal of radius 5 cm and height 4 cm is immersed it completely. Calculate the raise of the water in the glass?

The volumes of two cones of same base radius are 3600 cm³ and 5040 cm³. Find the ratio of heights.

A solid sphere and a solid hemisphere have equal total surface area. Prove that the ratio of their volume is 3\(\sqrt{3}\) : 4.

A toy is in the shape of a cylinder surrounded by a hemisphere. The height of the toy is 25 cm. Find the total surface area of the toy if its common diameter is 12 cm.

A jewel box is in the shape of a cuboid of dimensions 30 cm x 15 cm x 10 cm surmounted by a half part of a cylinder as shown in the figure. Find the volume and T.S.A. of the box.

A hemispherical section is cut out from one face of a cubical block  such that the diameter l of the hemisphere is equal to side length of the cube. Determine the surface area of the remaining solid.

As shown in figure a cubical block of side 7 cm is surmounted by a hemisphere. Find the surface area of the solid.

A solid sphere of radius 6 cm is melted into a hollow cylinder of uniform thickness. If the external radius of the base of the cylinder is 5 cm and its height is 32 cm, then find the thickness of the cylinder.

Find the number of coins, 1.5 cm in diameter and 2 mm thick, to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm.