Volume Formula

The following are some formulas used to calculate the volume of different three-dimension geometrical shapes: solid cylinder, hollow cylinder, prism, cone, pyramid, and sphere.

Volume of Cylinder

A cylinder is a solid that has two parallel faces which are congruent circles. These faces form the bases of the cylinder. The cylinder has one curved surface. The height of the cylinder is the perpendicular distance between the two bases.

The volume of a cylinder is given by the formula:

Volume = Area of base × height

V = r²h where r = radius of cylinder and h is the height or length of cylinder.

Volume of hollow cylinder

Sometimes you may be required to calculate the volume of a hollow cylinder or tube.

Volume of hollow cylinder

where R is the radius of the outer surface and r is the radius of the inner surface.

Volume of Prism

A prism is a solid that has two parallel faces which are congruent polygons at both ends. These faces form the bases of the prism. A prism is named after the shape of its base.

The other faces are in the shape of rectangles. They are called lateral faces.

Example :

When we cut a prism parallel to the base, we get a cross section of a prism. The cross section has the same size and shape as the base.

Example :

The volume of a right prism is given by the formula:

Volume of prism = Area of base × length

V = Al where A is the area of the base and l is the length or height of the prism.

Volume of Cone

A cone is a solid with a circular base. It has a curved surface which tapers (i.e. decreases in size) to a vertex at the top. The height of the cone is the perpendicular distance from the base to the vertex.

The volume of a cone is given by the formula:

Volume of cone = Area of base × height

V = where r is the radius of the base and h is the height of the prism.

Volume of Pyramid

A pyramid is a solid with a polygonal base and several triangular lateral faces. The pyramid is named after the shape of its base. For example, rectangular pyramid, triangular pyramid.

The lateral faces meet at a common vertex. The height of the pyramid is the perpendicular distance from the base to the vertex.

Example :

The volume of a pyramid is given by the formula:

Volume of pyramid = Area of base × height

V = where A is the area of the base and h is the height of the pyramid.

Volume of Sphere

A sphere is a solid in which all the points on the round surface are equidistant from a fixed point, known as the centre of the sphere. The distance from the centre to the surface is the radius.

Volume of sphere = where r is the radius.

A hemisphere is half a sphere, with one flat circular face and one bowl-shaped face.

Volume of hemisphere where r is the radius

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