Let us carry out a small activity. Take a coin. We know that coins are circular in shape. Now place another coin on the first coin. Then place another one and so on. You will see that when you place coins on top of one another, the solid that you get is a cylinder. Let us learn more about this three-dimensional solid object.

**Download Cylinder Formula Cheat Sheet Below**

## Cylinder

In geometry, a cylinder is a three-dimensional closed solid object. It has two round flat bases and one curved side. The curved surface is in the middle. Furthermore, the base and top surface are identical. That means the bases are always parallel and congruent to each other. It has no vertices. Objects shaped like cylinder are called cylindrical objects.

**Browse more Topics under Mensuration**

- Circles
- Polygons
- Rectangles and Squares
- Trapezium, Parallelogram and Rhombus
- Area and Perimeter
- Cube and Cuboid
- Cone
- Sphere

**Types of Cylinders**

**Right**: In this type, the two bases are over each other in the exact position and the axis (a line joining the centre of each base) is at the right angle to the base.

**Oblique**: In this type, one of the bases is sideways and the axis is not at the right angle to the base.

**Total Surface Area of a Cylinder**

Now, look at this figure carefully, we see that there are three faces. Two circles and one rectangle. When the ends are circles we call it a circular cylinder. In a circular cylinder, one circle is at the base the other is at the top. Furthermore, both these circles are of the same size. The rectangle face is the curved surface.

The area of the circle is πr², the area of two circles will be 2πr².

The area of the rectangle is length times the breadth. In this case, breadth is the circumference of the circle which is 2πr. And the length is the height of the cylinder, h.

Therefore, the area of the curved surface will be = 2πr × h = 2πrh square units.

So, the total area will be 2πr² + 2πrh, or

Total Surface Area of Cylinder = 2πr ( r + h ) square units

where r is the radius and h is the height (the distance between the two bases).

**The Volume of a Cylinder**

Volume is the amount of space occupied by the three-dimensional object. For a cylinder of radius r and height h, the volume will be,

V = πr²h cubic units

Let us calculate the volume for r = 3 cm and h = 5 cm.

We know that π = 3.14. So,

V = πr²h

= π ( 3²) 5

= π ( 9 ) 5

= (3. 14) (45)

= 141.30

Therefore volume is 141.30 cubic centimeters.

## Solved Problems For You

**Multiple Choice Questions**

**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?

- 54.06 cm
- 74.06 cm
- 34.06 cm
- 64.06 cm

**Answer:** B.

Given diameter = 2 cm or the r = 1 cm; height h =?. So,

V_{1} = πr²h = π(1)²h = πh cubic centimeters

For the hollow one, H = 15 cm; external diameter = 20 cm or external radius = 10 cm. Hence, internal diameter = 10-0.25 (thickness) = 9.75 cm. So,

V_{2} = π [ 10² – (9.75²) ] × 15 = 15π × 19.75 × 0.25 cubic centimeters

Also, V_{1} = V_{2 },

Therefore, h = 74.06 centimeters.

**Question 2.** If the lateral surface area of the cylinder is 500 cm² and its height is 10 cm, then calculate the radius of its base.

- 7.96 m
- or 7.96 cm
- 7.96 cm²
- 9.61 cm²

**Answer:** B.

The lateral surface area is A =2πrh.

Given A = 500 cm² and h = 10 cm. So,

A =2πrh

500 = 2 × 3.14 × r × 10

500 = 62.8r

r = 500/62.8

= 7.96

Therefore, the radius is 7.96 centimeters.

**Answer The Following**

**Question 3:** How to calculate the volume of a cylinder?

**Answer:** First, find the area of the base (which is a circle) by using the equation \( \pi r^{2}\) where r is the radius of the circular base. After that, multiply the area of the base by the height.

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

**Answer:** There is no fixed number for how many gallons or litres a cylinder can hold. It depends on the size (radius and height) of it. The bigger the cylinder the more gallons it can store.

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

**Answer:** It is the sum of the area of outer, bottom and the top surface. So, the general formula is \( 2 \pi rh + 2 \pi r^{2} \) square units.

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

**Answer:** It is \(2 \pi r (r_{1} + r_{2}) (r_{2} – r_{1} + h)\) square units. Here \(r_{1}\) is the inner radius \(r_{2}\) is the outer radius and h is the height.

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