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# Right Circular Cylinder

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 Sub Topics A right circular cylinder has its base perpendicular to its sides. If the line joining the centers of the Circles of a given cylinder is perpendicular to the bases, and then the cylinder is known as right circular cylinder. If a cylinder is having a radius and length, here length is denoted as height, then the volume of a right circular cylinder is given by V = $\pi$r2h, where r is the radius of a cylinder and h is the height of cylinder. The lateral surface area of a right circular cylinder is, A = 2$\pi$rh (this area is defines for lateral area or without top or bottom), And the total surface area of cylinder with top and bottom, A = 2$\pi$r2+ 2$\pi$rh, We can write it as: A = 2$\pi$r (r + h), Properties of a right circular cylinder are: The axis of a Right circular cylinder is the line joining the centers of cylinder which is having the bases. Example: - Calculate the volume and surface area of a right circular cylinder with r = 5" and h = 3"? Solution: We know that the Volume of Right Circular Cylinder = $\pi$r2h, And surface area of right circular cylinder = 2$\pi$r(r + h), We know that the value of $\pi$ = 3.14, Given, radius = 5, Height = 3, Putting the value in the formula, On putting the value we get, Volume of right circular cylinder = $\pi$r2h, V = 3.14 * (5)2 * 3, V = 3.14 * 25 * 3, V = 3.14 * 75, V = 235.5 inch3, Surface area of right circular cylinder = 2$\pi$r (r + h), SA = 2$\pi$r (r + h), = 2 * 3.14 * 5 (5 + 3), = 2 * 3.14 * 5 (8), = 2 * 3.14 * 40, = 251.2 inch2.

## Lateral Surface Area of Right Circular Cylinder

A cylinder which has base and sides and whose base is perpendicular to the cylinder sides is known as a Right Circular Cylinder. A right circular cylinder has bases just like a Circle. The Lateral Surface Area Of Right Circular Cylinder is calculated by using the following formula:

The Lateral Surface Area of Right Circular Cylinder = 2$\pi$rh,

Where, r is the radius of a right circular cylinder,

H is the height of a right circular cylinder,

And the value of $\pi$ is 3.14.

Now we will see how to find the Lateral Surface Area of Right Circular Cylinder?

For finding the Lateral Surface Area of Right Circular Cylinder we have to follow some of the steps:

Step 1: For finding the lateral surface area of a right circular cylinder firstly we find the radius of a given cylinder.

Step 2: After than we find the height of a right circular cylinder.

Step 3: Then we put all the values in the formula and we get the lateral surface area of a right circular cylinder.

Suppose we have the radius of right circular cylinder is 15 inch and the height of a right circular cylinder is 25 inch then, what is the lateral surface area of a right circular cylinder.

The Lateral Surface Area of Right Circular Cylinder = 2$\pi$rh.

Step 1: First we find the radius of a right circular cylinder.
Here radius of right circular cylinder is 15 inch.

Step 2: The height of a right circular cylinder.

Here height is 25 inch.

The Lateral Surface Area of Right Circular Cylinder = 2$\pi$rh,

Surface area = 2$\pi$ * (15) * 25,

Surface area = 2$\pi$ * 375,

We know that the value of ‘$\pi$’ is 3.14.

So put the value of ‘$\pi$’ in the formula:

Surface area = 2 * 3.14 * 375,

Surface area = 6.28 * 375,

Surface area = 2355 inch2,

So the lateral Surface area of a right circular cylinder is 2355 inch2.

## Volume of Right Circular Cylinder

A Right Circular Cylinder is a type of cylinder which has base and sides and whose base is perpendicular to the cylinder sides. A right circular cylinder has base just like a Circle. The Volume Of A Right Circular Cylinder is calculated by using the following formula:

The volume of right circular cylinder = $\pi$r2h,

Where, ‘r’ is the radius of a right circular cylinder,

H is the height of a right circular cylinder,

And the value of $\pi$ is 3.14.

Now we see how we find the volume of a right circular cylinder.

For finding the volume of a right circular cylinder we have to follow of some of the steps:

Step 1: For finding the volume firstly we have to find the radius of a right circular cylinder.

Step 2: If we find radius then we have find the height of right circular cylinder.

Step 3: After putting these values in the formula we get required volume of right cylinder.

Suppose we have to find the volume of right circular cylinder where radius of right circular cylinder is 5 inch and the height of a right circular cylinder is 8 inch.

Then,

The volume of right circular cylinder = ⊼r2h,

Step 1: Find the value of radius.

Here radius of right circular cylinder is 5 inch.

Step 2: Now the height of a right circular cylinder.

Here height is 8 inch.

The volume of right circular cylinder = $\pi$r2h,

Volume = $\pi$ * (5)2 * 8,

Volume = $\pi$ * 25 * 8,

Now we put the value of ‘⊼’ in the given formula:

We know that the value of ⊼ is 3.14.

So put the value of ‘⊼’ in the formula:

Volume = 3.14 * 25 * 8,

Volume = 3.14 * 200,

Volume = 628 inch3.

So the volume of a right circular cylinder is 628 inch3.

## Total Surface Area of Right Circular Cylinder

A cylinder which has circular base and the axis joining the two centers of the perpendicular bases to the plane is known as a Right Circular Cylinder. The total surface area of right circular cylinder is calculated by using the following formula:

The total surface area of right circular cylinder = 2$\pi$rh + 2$\pi$r2,

Where, r is the radius of a right circular cylinder,

H is the height of a right circular cylinder,

Now we have to follow some of the steps for finding the total Surface Area of Right Circular Cylinder?

The steps are as follows:

Step 1: First we find the radius of a right circular cylinder.

Step 2: After that we find the height of a right circular cylinder.

Step 3: The total surface area of a right circular cylinder we find the radius and height of other side of a right circular cylinder.

Step 4: After that we have to add both the values of a right circular cylinder.

Step 5: Then we put all the values in the formula and we get the total surface area of a right circular cylinder.

We have the radius of right circular cylinder which is 20 inch and the height of a right circular cylinder is 35 inch then, what is the total surface area of a right circular cylinder.

The total surface area of right circular cylinder = 2$\pi$rh + 2$\pi$r2,

In the first Step we see the radius of a right circular cylinder.

Here radius of right circular cylinder is 20 inch.

In the Step 2 we find the height of a right circular cylinder.

Here height is 35 inch.

The total surface area of right circular cylinder = 2$\pi$rh + 2$\pi$r2,

Total Surface area = 2$\pi$ * 20 * 25 + 2$\pi$ * (20)2,

Total Surface area = 2$\pi$ * 500 + 2$\pi$ * 400,

We know that the value of $\pi$ is 3.14.

Total Surface area = 2 * 3.14 * 500 + 2 * 3.14 * 400,

Total Surface area = 3140 + 2512,

Total Surface area = 5652 inch2,

So the lateral Surface area of a right circular cylinder is 5652 inch2.