Mathematics Questions

A cylindrical tank of radius 7 m and height 10 m is full of water. If this water is poured into a rectangular tank of length 22 m and width 10 m, what will be the height of water?

Find the volume of a hollow cylinder with external radius 5 cm, internal radius 4 cm, and height 10 cm.

If the radius of a cylinder is doubled and the height is halved, what is the ratio of the new volume to the original volume?

A solid cone of height 24 cm and radius of base 6 cm is melted and reshaped into a sphere. Find the radius of the sphere.

The sum of length, breadth, and height of a cuboid is 19 cm and its diagonal is 11 cm. Find its volume if the surface area is not needed but related? (Wait, let's use a standard volume problem). A cuboid has dimensions in the ratio 3:2:1 and volume 1296 cm³. Find the length.

A hemisphere and a cone have equal bases. If their heights are also equal (height of hemisphere being its radius), find the ratio of their volumes.

The volume of two spheres are in the ratio 64:27. Find the ratio of their surface areas.

A well of diameter 2 m is dug 14 m deep. The earth taken out is spread evenly to form a platform 5 m by 2 m. Find the height of the platform.

A right circular cone is 3.6 cm high and its base radius is 1.6 cm. It is melted and recast into a right circular cone with base radius 1.2 cm. Find its height.

How many bullets can be made out of a lead cylinder 28 cm high and 6 cm radius, each bullet being 1.5 cm in diameter?

The base of a right pyramid is a square of side 10 cm. If its volume is 400 cm³, find its total height.

A metal pipe has an external diameter of 4 cm and internal diameter of 3 cm. If its length is 20 cm, find the volume of metal used.

A conical tent is 9 m high and the radius of its base is 12 m. What is the cost of rice required to fill the tent if 1 m³ rice costs Rs 100?

If the radius of a sphere is increased by 10%, what is the percentage increase in its volume?

A solid lead ball of radius 7 cm was melted and then drawn into a wire of diameter 0.2 cm. Find the length of the wire.

The volume of a right circular cone is 9856 cm³. If the diameter of the base is 28 cm, find its slant height.

A hemispherical bowl has an internal radius of 9 cm and is full of liquid. The liquid is to be filled into cylindrical bottles of diameter 3 cm and height 4 cm. How many bottles are required?

The volume of a prism with an equilateral triangular base is 40√3 cm³. If the side of the triangle is 4 cm, find the height of the prism.

Water flows out of a pipe of cross-section 4 cm² at a speed of 10 cm/s. How many liters of water will flow out in 1 minute?

If the areas of three adjacent faces of a cuboid are x, y, and z, then the volume V is given by: