**Volume of Cylinder**

**What is Volume?**

The volume of a 3-dimensional shape is the amount of space it occupies. It can also be defined as the amount of space contained within the solid.

**What is the volume of a cylinder?**

The volume of a cylinder is a fundamental concept in geometry that measures the amount of space enclosed by a cylinder. A cylinder is a three-dimensional geometric shape with two parallel circular bases and a curved surface connecting the bases. It is often encountered in real-life objects such as cans, pipes, and containers.

It is the product of the area of its circular base and its height.

**Volume of cylinder**

For a cylinder with r as the radius of its circular base and h as height,

Volume of cylinder = Area of circular base x Height

Volume of cylinder = πr2 x h

In this formula, “π” represents the mathematical constant pi, which is approximately 3.14159. “r” denotes the radius of the circular base of the cylinder, and “h” represents the height of the cylinder. The radius is the distance from the center of the circular base to its edge, while the height is the perpendicular distance between the two bases.

To find the volume, we square the radius (r²) and multiply it by the height (h) and the value of pi (π). This formula holds true for cylinders of any size or proportions.

It is important to note that the units used for the radius and height must be consistent. For example, if the radius is measured in centimeters, the height should also be in centimeters to obtain the volume in cubic centimeters.

The volume of a cylinder is significant in various applications. For instance, it helps determine the capacity of cylindrical containers, calculate the amount of liquid or gas that can be stored, and understand the displacement of fluids in engineering and physics. Additionally, the volume of a cylinder is a fundamental concept in solid geometry and plays a crucial role in understanding the properties and relationships of three-dimensional shapes.

**Solved examples on Volume of Cylinder:**

**Example 1.** Find the volume of a cylinder with a radius of 4 cm and a height of 10 cm.

Solution:

Using the formula for the volume of a cylinder: Volume = π x r² x h

Given:

Radius (r) = 4 cm

Height (h) = 10 cm

Substituting the given values into the formula:

Volume = π x (4 cm)² x (10 cm)

Volume = 3.14159 x 16 cm² x 10 cm

Volume = 502.65408 cm³ (rounded to five decimal places)

Therefore, the volume of the cylinder is approximately 502.65408 cm³.

**Example 2. **A cylindrical water tank has a diameter of 1.5 meters and a height of 2 meters. Calculate the volume of the tank.

Solution:

First, we need to find the radius since the diameter is given. The radius (r) is half the diameter.

Given:

Diameter = 1.5 meters

Height (h) = 2 meters

Calculating the radius:

Radius (r) = Diameter / 2 = 1.5 meters / 2 = 0.75 meters

Using the volume formula:

Volume = π x r² x h

Substituting the values:

Volume = 3.14159 x (0.75 meters)² x 2 meters

Volume = 3.14159 x 0.5625 square meters x 2 meters

Volume = 3.534291 square meters x 2 meters

Volume = 7.068582 cubic meters

Therefore, the volume of the cylindrical water tank is approximately 7.068582 cubic meters.

**Frequently asked questions on Volume of Cylinder:**

- What is the volume of a cylinder?

Answer: The volume of a cylinder refers to the amount of space enclosed by a cylinder. It is a measure of the three-dimensional capacity of the cylinder.

- How do you calculate the volume of a cylinder?

Answer: The volume of a cylinder can be calculated using the formula: Volume = π x r² x h, where “π” represents the mathematical constant pi (approximately 3.14159), “r” is the radius of the cylinder’s base, and “h” is the height of the cylinder.

- Can you explain the concept of radius and height in a cylinder?

Answer: In a cylinder, the radius (r) is the distance from the center of the circular base to its edge, and the height (h) is the perpendicular distance between the two bases.

- What are the units of volume for a cylinder?

Answer: The units of volume for a cylinder are derived from the units of the radius and height. For example, if the radius and height are both measured in centimeters, the volume will be in cubic centimeters (cm³).

- Can the volume of a cylinder be negative?

Answer: No, the volume of a cylinder cannot be negative. Volume is a measure of space, which is always positive or zero.