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>Hello Sohib EditorOnline, today we will discuss about how to calculate the height of a cylinder. As we know, a cylinder is a three-dimensional shape that can be found in many objects around us, such as pipes, cans, and even towers. Knowing the height of a cylinder is important for many reasons, including calculating the volume and understanding its capacity. In this article, we will explore the step-by-step process of calculating the height of a cylinder. Let’s get started!

1. Understanding the Cylinder Shape

Before we start calculating the height of a cylinder, it is important to understand its basic shape. A cylinder consists of two congruent circular bases and a curved lateral surface that connects them. The height of the cylinder is the perpendicular distance between the two circular bases. See the image below for a clearer understanding:

Image by Math is Fun

You can see that the height of the cylinder is represented by h, while the radius of the circular base is represented by r.

1.1. Deriving the Cylinder Volume Formula

Before we dive into calculating the height of the cylinder, let’s first derive the formula for calculating its volume. The formula for the volume of a cylinder is:

V = πr²h

The formula can be derived by multiplying the area of the circular base, which is πr² by the height of the cylinder h. Therefore, the volume of the cylinder is the space that is enclosed within its curved lateral surface.

2. Calculating the Height of a Cylinder

Now that we have a basic understanding of the cylinder shape and its volume formula, we can start calculating the height of a cylinder. To calculate the height, we need to know the radius of the circular base and the volume of the cylinder. Let’s explore the process of calculating the height step-by-step:

2.1. Finding the Radius of the Circular Base

The first step in calculating the height of a cylinder is to find the radius of the circular base. This can be done easily if we have the diameter of the circular base. To find the radius, we simply divide the diameter by 2:

r = d/2

If we do not have the diameter, we can measure the circumference of the circular base and use the following formula to find the radius:

r = C/2π

Where C is the circumference of the circular base, and π is a constant value of approximately 3.14.

2.2. Finding the Volume of the Cylinder

Once we have found the radius of the circular base, we can now find the volume of the cylinder using the formula:

V = πr²h

If we know the volume of the cylinder, we can rearrange the formula to solve for the height h:

h = V / (πr²)

Therefore, to find the height of the cylinder, we need to divide the volume of the cylinder by the area of the circular base, which is πr².

2.3. Examples of Calculating the Height of a Cylinder

Let’s now look at some examples to understand better how to calculate the height of a cylinder. In each example, we will be given the radius of the circular base and the volume of the cylinder:

2.3.1. Example 1

A cylinder has a radius of 6 cm and a volume of 678.58 cm³. What is the height of the cylinder?

First, let’s find the area of the circular base:

πr² = π x 6² = 113.1 cm²

Now, let’s use the formula we derived earlier to find the height:

h = V / (πr²) = 678.58 / 113.1 ≈ 6 cm

Therefore, the height of the cylinder is approximately 6 cm.

2.3.2. Example 2

A cylinder has a radius of 5 in and a volume of 392.7 in³. What is the height of the cylinder?

First, let’s find the area of the circular base:

πr² = π x 5² = 78.54 in²

Now, let’s use the formula we derived earlier to find the height:

h = V / (πr²) = 392.7 / 78.54 ≈ 5 in

Therefore, the height of the cylinder is approximately 5 in.

3. Frequently Asked Questions (FAQ)

3.1. What is a cylinder?

A cylinder is a three-dimensional shape that has two congruent circular bases and a curved lateral surface that connects them.

3.2. Why is it important to know the height of a cylinder?

Knowing the height of a cylinder is important for many reasons, including calculating the volume and understanding its capacity.

3.3. How do you calculate the height of a cylinder?

To calculate the height of a cylinder, you need to know the radius of the circular base and the volume of the cylinder. You can then use the formula h = V / (πr²) to find the height.

3.4. What is the formula for the volume of a cylinder?

The formula for the volume of a cylinder is V = πr²h.

3.5. How do you find the radius of a circular base?

If you have the diameter of the circular base, you can find the radius by dividing the diameter by 2. If you do not have the diameter, you can measure the circumference of the circular base and use the formula r = C/2π to find the radius.

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