10 Examples of Volume in Mathematics

Volume is a fundamental concept in mathematics that helps us measure the amount of space occupied by a three-dimensional object.

In this article, we will discuss ten examples of volume in mathematics.

Examples of Volume

These are 10 examples of volume.

1: Volume of a Cube

Find the volume of a cube with side length of 5 units.

Solution: The formula for the volume of a cube is V = side^3. Plugging in the side length, V = 5^3 = 5 × 5 × 5 = 125 cubic units.

2: Volume of a Rectangular Prism

Calculate the volume of a rectangular prism with dimensions: length = 8 units, width = 4 units, and height = 3 units.

Solution: The formula for the volume of a rectangular prism is V = length × width × height. Plugging in the values, V = 8 × 4 × 3 = 96 cubic units.

3: Volume of a Cylinder

Determine the volume of a cylinder with a radius of 2 units and a height of 6 units.

Solution: The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height. Plugging in the values, V = π × (2^2) × 6 = 24π cubic units.

4: Volume of a Sphere

Calculate the volume of a sphere with a radius of 4 units.

Solution: The formula for the volume of a sphere is V = (4/3)πr^3, where r is the radius. Plugging in the radius, V = (4/3)π × (4^3) = 256π cubic units.

5: Volume of a Cone

Find the volume of a cone with a radius of 3 units and a height of 5 units.

Solution: The formula for the volume of a cone is V = (1/3)πr^2h. Plugging in the values, V = (1/3)π × (3^2) × 5 = 45π cubic units.

6: Volume of a Triangular Prism

Determine the volume of a triangular prism with base dimensions: base length = 6 units, base width = 4 units, and height = 8 units.

Solution: The formula for the volume of a triangular prism is V = (1/2)Bh, where B is the base area and h is the height. The base area is (1/2) × 6 × 4 = 12 square units. Plugging in the values, V = 12 × 8 = 96 cubic units.

7: Volume of a Pyramid

Calculate the volume of a square pyramid with a base side length of 10 units and a height of 6 units.

Solution: The formula for the volume of a pyramid is V = (1/3)Bh, where B is the base area and h is the height. The base area is 10 × 10 = 100 square units. Plugging in the values, V = (1/3) × 100 × 6 = 200 cubic units.

8: Volume of a Rectangular Pyramid

Find the volume of a rectangular pyramid with dimensions: length = 5 units, width = 3 units, and height = 7 units.

Solution: The formula for the volume of a rectangular pyramid is V = (1/3)lwh, where l is the length, w is the width, and h is the height. Plugging in the values, V = (1/3) × 5 × 3 × 7 = 35 cubic units.

9: Volume of a Prismatic Tank

Calculate the volume of a rectangular tank with a length of 12 feet, a width of 8 feet, and a height of 4 feet.

Solution: Using the formula for the volume of a rectangular prism, V = length × width × height, V = 12 × 8 × 4 = 384 cubic feet.

10: Volume of an Irregular Shape

Find the volume of an irregularly shaped container by filling it with water and measuring the amount of water used, which is 5000 cubic centimeters.

Solution: By filling the container with water and measuring the amount used, we determine the volume to be 5000 cubic centimeters.