Mensuration Il Mathematics - Mensuration Il

A sphere and a cone have the same radii. If their volumes are also equal, prove that the height of the cone is twice its radius.

Find the radius of the sphere whose surface area is equal to its volume .

Find the volume of the hollow sphere whose inner diameter is 8 cm and the thickness of the material of which it is made is 1 cm .

Find the cost of painting a hemispherical dome of diameter 10 m at the rate of Rs 1.40 per square metre.

Find the total surface area and volume of a hemisphere whose radius is 10 cm.

The radius and height of a cylinder, a cone and a sphere are same. Calculate the ratio of their volumes.

A hollow metallic cylindrical tube has an internal radius of 3.5 cm and height 21 cm. The thickness of the metal tube is 0.5 cm. The tube is melted and cast into a right circular cone of height 7 cm. Find the radius of the cone, correct to one decimal place.

A buoy is made in the form of a hemisphere surmounted by a right circular cone whose circular base coincides with the plane surface of the hemisphere. The radius of the base of the cone is 3.5 m and its volume is two-third the volume of hemisphere. Calculate the height of the cone and the surface area of the buoy, correct to two decimal places.

A hollow metallic cylindrical tube has an internal radius of 3.5 cm and height 21 cm. The thickness of the metal tube is 0.5 cm. The tube is melted and cast into a right circular cone of height 7 cm. Find the radius of the cone, correct to one decimal place.

A cylindrical bucket, whose base radius is 20 cm, is filled with water to a height of 25 cm. A heavy iron spherical ball of radius 10 cm is dropped to submerge completely in water in the bucket. Find the increase in the level of water.

A cylindrical beaker of 7 cm diameter is partly filled with water. Determine the number of spherical marbles of diameter 1.4 cm that are to be submerged in it to raise the water level by 5.6 cm