Volume of a Cylinder

A three-dimensional geometrical figure which is made up of two congruent or equal and parallel identical bases is known as a cylinder. A cylinder is categorized into three types based on the sides and bases of the cylinder. They are the right circular cylinder, oblique cylinder, hollow cylinder, and elliptic cylinder. The volume of a cylinder is the total space or region that a cylinder can hold inside it. Mathematically, the volume of a cylinder is the total amount of cubic units that can be filled inside a cylinder. The formula used to calculate the volume of a cylinder is a * h where ‘h’ is the height of the cylinder and ‘a’ is the area of the base. Each type of cylinder has a different formula for the volume. For instance, the volume of an oblique cylinder is πr. πr.h, where ‘r’ is the radius of the cylinder and ‘h’, is the height of the cylinder. We shall solve some examples based on the volume of a cylinder in the coming sections.

Examples

To recall, the formula used to calculate the volume of a cylinder is a * h where ‘h’ is the height of the cylinder and ‘a’ is the area of the base. Some examples related to the volume of a sphere are:

Example 1: Find the volume of the cylinder if the area of base and height of the cylinder is 3 cm and 8 cm respectively?

Solution:

                  Given that,

                  Area of base = 3 cm

                  Height of Cylinder = 8 cm

                  Using the formula, the volume of cylinder = a * h.

                  8 * 3 = 24 cm cubic units.

                  Hence, the volume of the cylinder for the given area of base and height is 24 cm cubic units.

Example 2: Find the volume of the cylinder if the area of base and height of the cylinder is 9 cm and 7 cm respectively?

Solution:

                  Given that,

                   Area of base = 9 cm

                   Height of Cylinder = 7 cm

                   Using the formula, the volume of cylinder = a * h.

                   9 * 7 = 63 cm cubic units.

                     Hence, the volume of the cylinder for the given area of base and height is 63 cm cubic units.

Volume of a Sphere

A three-dimensional shape that has no edges or vertices in it is known as a sphere. A sphere looks similar to a circle, but a circle is a two-dimensional shape. More often than not, our earth is considered a sphere but it is a spheroid. Now, the volume of a sphere is the total amount of measurement that a sphere can hold inside it. It can also be defined as the total amount of cubic units that a sphere can hold inside it.
The mathematical formula to find the volume of a sphere is deduced by the volume of the cone and the volume of a cylinder. Thus, the formula for the volume of a sphere is (4/3)πr.r.r. where ‘r’ is the radius of the sphere. A sphere is also classified into two types based on its radius. They are Solid spheres and Hollow spheres. The formula for the solid sphere is the same for the normal sphere i.e.(4/3)πr.r.r. We shall cover some examples based on the volume of the sphere in the next section.

Examples

The mathematical formula to find the volume of a solid sphere is (4/3)πr.r.r where ‘r’ is the radius of the sphere:

Example 1: Find the volume of the cylinder if the radius of the sphere is 4 cm. Take the value of π as 3.14.

Solution:

                   Given that,

                   Radius of sphere = 4 cm.

                   Using the formula of volume of sphere = (4/3)πr.πr.πr

                   4/3. 3.14 * 4 * 4 * 4 = 4/3 * 200.96.

                   4/3 * 200.96 = 261.48 cubic units.

                  Hence, the volume of a sphere is equivalent to 261.48 cubic units. If you want to develop more skills with amazing math concepts, visit Cuemath.