What is the formula for the volume and surface area of a cylinder?

The formula for calculating the volume of a cylinder is:

V= πr²h

The formula for calculating the surface area of cylinder is a little harder to remember:

S.A = 2πr² + 2πrh

V stands for volume (space inside a 3D shape).

S.A stands for the Surface Area (space around the outside of a 3D shape).

r stands for the radius of the cylinder (the distance halfway across the centre of the circle).

h is the height or length of the cylinder.

Π is Pi (mathematical constant equal to 3.14 to 3 significant figures).

Let’s take a look at an example of working out the surface area and volume of a cylinder.

Example 1

The diagram shows a tin of soup. Work out the volume and surface area of the tin.

Let’s begin by finding the volume.

All you need to do is substitute the radius and height into the formula above. The radius of the cylinder is 6cm and the height is 15cm

So r = 6 and h = 15

V= πr²h

= π × 6² × 15

= 1696 cm³ to the nearest whole number.

Now let’s calculate the surface area of the cylinder. Again all you need to do is substitute r = 5 cm and h = 15 cm into the formula for surface area.

S.A = 2πr² + 2πrh

S.A = 2 × π × 6² + 2 × π × 6 × 15

S.A = 792 cm² to the nearest integer.

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