Mensuration

A sphere, a cylinder and a cone have the same radius and same height. Find the ratio of their volumes.

What is the volume of a right circular cone whose lateral surface area is 120 cm² and base radius is 6 cm?

A cube of side 6 cm is cut into 8 identical smaller cubes. What is the side of each smaller cube?

A pyramid has a height of 15 cm and its base is a right-angled triangle with sides 5 cm, 12 cm, and 13 cm. Find its volume.

The volume of a sphere is doubled. What is the ratio of the new radius to the old radius?

A cubical block of metal weighs 16 kg. What is the weight of another block of the same metal whose each side is double that of the first block?

Find the volume of a right circular cylinder whose curved surface area is 264 cm² and height is 14 cm.

The radii of the ends of a frustum of a cone are 14 cm and 7 cm, and its height is 6 cm. Find its volume.

A solid cylinder has a total surface area of 462 cm². Its curved surface area is one-third of its total surface area. Find its volume.

A conical vessel, with internal radius 5 cm and height 24 cm, is full of water. The water is emptied into a cylindrical vessel with internal radius 10 cm. Find the height to which the water rises.

A hemispherical tank full of water is emptied by a pipe at the rate of 25/7 liters per second. How much time will it take to empty half the tank, if it is 3 m in diameter?

The internal and external diameters of a hollow hemispherical vessel are 24 cm and 25 cm respectively. The cost to paint 1 cm² of the surface is Rs 0.05. Find the volume of material.

Water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/h. How much area will it irrigate in 30 minutes, if 8 cm of standing water is needed?

A solid is in the form of a cylinder with hemispherical ends. The total height of the solid is 19 cm and the diameter of the cylinder is 7 cm. Find the volume of the solid.

A circus tent is cylindrical to a height of 3 m and conical above it. If its diameter is 105 m and the slant height of the conical portion is 53 m, find the total volume of air inside.

A metallic sphere of radius 10.5 cm is melted and then recast into small cones, each of radius 3.5 cm and height 3 cm. Find the number of cones.

The ratio of the volumes of two cones is 1:4 and their diameters are in the ratio 4:5. Find the ratio of their heights.

A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones.

A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15 cm by 10 cm by 3.5 cm. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand.

A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which is surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that 1 cm³ of iron has approximately 8g mass.