# 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.

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