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# Right Circular Cylinder

A right circular cylinder is one such geometric shape which is used frequently in real life. A cylinder has a closed circular surface having two parallel bases on both the ends. All the points lying on the closed circular surface is at a fixed distance from a straight line known as the axis of the cylinder. The two circular bases of the right angled triangle have same radius and are parallel to each other.

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## Right Circular Cylinder Formula

A surface is generated by a line which intersects a fixed circle and is perpendicular to the plane of the circle is said to be right circular cylinder. A right circular cylinder has two circular bases which are of same radius and are parallel to each other.

Let r be the radius and h be the perpendicular height of a right cylinder as shown below,

### Volume:

The volume of a right cylinder is given by the product of the area of the top or bottom circle and the height of the cylinder. The volume of a right cylinder is measured in terms of cubic units.

Volume = area of the circle $\times$ height of the cylinder

= $\pi r^2$ $\times$ h

= $\pi r^2$ h

Volume = $\pi r^2$ h cubic units

### Surface Area:

The sum of lateral surface area and the base area of both the circles will give the surface are of the right circular cylinder.

Surface area = 2 $\pi$ r (h + r) square units

### Lateral Area:

The surface area of a closed right circular cylinder is the sum of the area of the curved surface and the area of the two bases. The curved surface that joins the two circular bases is said to be lateral surface of the right circular cylinder.

Lateral area = 2 $\pi$ r h square units

## How to Find the Volume of a Right Circular Cylinder?

Given below are some of the examples to find the volume of a right circular cylinder.

### Solved Examples

Question 1: Find the volume of a right cylinder, if the radius and height of the cylinder are 20 cm and 30 cm respectively.
Solution:

Volume of a right cylinder = $\pi r^2$ h cubic units

Given that, r = 20 cm

h = 30 cm

Volume = 3.14 $\times$ 202 $\times$ 30

= 3.14 $\times$ 20 $\times$ 20 $\times$ 30

= 37680

So, the volume of the given right cylinder is 37680 cubic cm.

Question 2: The radius and height of a right cylinder is given as 5 m and 6.5 m respectively. Find the volume of the right cylinder.
Solution:

Volume of a right cylinder = $\pi r^2$ h cubic units

Given that, r = 5 m

h = 6.5 m

Volume = 3.14 $\times$ 52 $\times$ 6.5

= 3.14 $\times$ 25 $\times$ 6.5

= 510.25

So, the volume of the given right cylinder is 510.25 cubic m.

Question 3: A right circular cylinder inscribed in a sphere of radius 10 cm. Find the volume of the shaded region. Give your answer in terms of $\pi$ and rounded to the nearest tenth.

Solution:

Radius of cylinder (r) = 5 cm
Radius of sphere (R) = 10 cm, therefore height of cylinder (h) = 20 cm

From figure: Volume of the shaded region can be found by subtracting the volume of sphere from the volume of cylinder.

=> Volume of the shaded region = Volume of sphere - Volume of cylinder

Volume of sphere = $\frac{4}{3}$ $\pi$ $R^3$

= $\frac{4}{3}$ $\pi$ $\times$ (10)$^3$

= $\frac{4}{3}$ $\pi$$\times$ 1000

= 1333.33$\pi$

Volume of cylinder = $\pi$ $r^2$ h

= $\pi$(25)(20)

= 500$\pi$

Now,

Volume of the shaded region = 1333.33$\pi$ -  500$\pi$

= 833.33 $\pi$

Using $\pi$ = 3.14 and rounding to the nearest tenth, we get

Volume =  833.33 $\times$ 3.14 = 2616.65

Hence, the Volume of the shaded region is 2616.65 cm3

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