**Find The Surface Area Of A Cylinder Step By Step**

###### To Learn How To Find The Surface Area Of A Cylinder first we want you to take a look at what is a Cylinder exactly.

### Cylinder:Â

**Let’s do some activities. Take a ring plate. We know that the ring has a circular shape. Now, place another ring plate on the first one and continue to place some.**

When placing such a ring, you will see that the resulting structure is a three-dimensional cylinder. Now let’s learn How To Find The Surface Area Of A Cylinder.

#### Â **Learn â‡’ How To Find The Diameter Of A CircleÂ **

**Cylinder**

A cylinder is a three-dimensional object with two round flat bottoms and a curved side. It has a curved surface in the middle. The bottom and top surfaces are the same. This means that the bases are always parallel and coincide with each other. It has no peak.

### Total Surface Area of a Cylinder

Now, if we look closely at this picture, we will see that the cylinder has three faces. Two circles and a rectangle. One circle is below the cylinder and the other circle is above. Two circles of the same size.

- The rectangle face is the curved surface of the cylinder. So,
- So the area of the cylinder will be: 2Ï€rÂ² + 2Ï€rh, or
- Total Surface Area of Cylinder = 2Ï€r ( r + h )

Where r is the radius and h is the height of the cylinder (the distance between two substrates).

### The Volume of a Cylinder

Suppose if we have a cylinder of radius r and height h, then the volume will be,

V = Ï€rÂ²h

V is the amount of space occupied by the three-dimensional object.Let us see an example to find out the volume of a cylinder.As we know Ï€ = 3.14.So, let us find the volume of a Â cylinder that has the radius 3 cm and height 5 cm.

Now,

V = Ï€rÂ²h

=Â Ï€ ( 3Â²) 5

=Â Ï€ ( 9 ) 5

= (3.14) (45)

= 141.30 cmÂ³

### Right and Oblique Cylinder

### Solved Examples For You

**Question 1.**What length of a solid cylinder which is 2 cm in diameter must be taken to recast into a hollow cylinder of external diameter 20 cm, 0.25 cm thick and 15 cm long?Answer: B.The diamet er of the solid cylinder = 2 cm or the radius = 1 cm; height h =?

V1 = Ï€rÂ²h = Ï€(1)Â²h = Ï€hÂ³

For the hollow cylinder, H = 15 cm; external diameter = 20 cm or external radius = 10 cm.Hence, internal diameter = 10-0.25 (thickness+ = 9.75 cm.Therefore,

V2 =Â Ï€ [ 10Â²Â â€“ (9.75Â²) ]Â Ã— 15 = 15Ï€Â Ã— 19.75Â Ã— 0.25

Also, V1 = V2, which gives

h = 74.06 cm

**Question 2.**If the lateral surface of the cylinder is 500 cmÂ² and its height is 10 cm, then find the radius of its base.

Answer: B.The lateral surface area is A =2Ï€rh.The curved surface area is A =Â 500 cmÂ² and its height is 10 cm, hence

A =2Ï€rh

500 = 2Â Ã— 3.14Â Ã— rÂ Ã— 10

500 = 62.8r

r = 500/62.8

= 7.96

Therefore the radius of the cylinder is 7.96 cm

**Question 3.**How to find the volume of a cylinder?

Answer: To find the volume of the cylinder, firstly, find the area of the base (which is a circle) by using the equation \pi r^{2}Ï€r2 where r is the radius o the circular base.After that, multiply the area of the base by the height of the cylinder to know the volume of the 9base.

**Question 4.**Â How many gallons are there in a cylinder?

Answer: The cylinder capacity is not fixed. How many gallons or liters it can hold depends on the size (radius and height) of the cylinder. The larger the cylinder, the greater the number of gallons that can be stored.

**Question 5.**Â State the formula of the total surface area of a cylinder?

Answer: The total surface area of the cylinder refers to the outer surface of the cylinder plus the lower and upper surfaces of the cylinder. So, the general formula of the total surface area of a cylinder is 2 \pi rh + 2 \pi r^{2} 2Ï€rh+2Ï€r2.

**Question 6.**Â What is the total surface area of the hollow cylinder?

Answer: The total surface area of a hollow cylinder is 2 \pi r (r_{1} + r_{2}) (r_{2} â€“ r_{1} + h)2Ï€r(r1+r2)(r2â€“r1+h).Here r_{1}r1 is the inner radius r_{2}r2 is the outer radius and h is the height.9999999999999999999