Mathematics Questions

A spherical glass vessel has a cylindrical neck 8 cm long, 2 cm in diameter; the diameter of the spherical part is 8.5 cm. Find the volume of water it can hold.

A storage tank consists of a circular cylinder with a hemisphere adjoined on either end. If the external diameter of the cylinder be 1.4 m and its length be 8 m, find the cost of painting it on the outside at the rate of Rs 10 per m²? (Wait, volume question requested). Find the volume of the tank.

A cylindrical pipe has inner diameter 4 cm and water flows through it at 20 m/min. How long would it take to fill a conical vessel of radius 40 cm and depth 72 cm?

A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter d of the hemisphere is equal to the edge of the cube. Find the volume of the remaining solid.

The rain water from a roof of 22 m × 20 m drains into a cylindrical vessel having diameter of base 2 m and height 3.5 m. If the vessel is just full, find the rainfall in cm.

Find the volume of the largest right circular cone that can be cut out of a cube whose edge is 9 cm.

A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. If the radius of the cylinder is 60 cm and its height is 180 cm, find the volume of water left in the cylinder.

If the radius of the base of a cone is halved, keeping the height same, what is the ratio of the volume of the reduced cone to that of the original cone?

What is the volume of a sphere whose surface area is 36π cm²?

Find the volume of a right circular cylinder with height 20 cm and radius 7 cm.

A cuboid of volume 96 cm³ has a length of 8 cm and a breadth of 3 cm. Find its height.

A pyramid has a volume of 100 cm³. If its height is 12 cm, find the area of its base.

The volume of a hemisphere is 2425.5 cm³. Find its radius.

Find the volume of a prism whose base is a triangle with base 6 cm and height 4 cm, and the length of the prism is 15 cm.

If the volume of a cube is 1000 cm³, what is its total surface area?

Calculate the volume of a cone with radius 3.5 cm and height 12 cm.

A metal sphere of radius 6 cm is melted into 27 small spheres. Find the radius of each small sphere.

The volume of a cylindrical container is 448π cm³ and its height is 7 cm. Find its curved surface area.

If the height of a cone is tripled and its radius is doubled, the volume becomes how many times the original?

Find the volume of a right circular cone with slant height 25 cm and base radius 7 cm.