Find the Area of Shaded Circular Rings

The formula for the area, A, of a circle in terms of its radius, r, is given by:

A = πr²

In this activity, we will use the pie symbol on our calculators in our calculations.  If you do not have a scientific calculator, you can always use one online.

To work out the shaded area shown below, we must work out the area of the outer circle and subtract the area of the inner circle.

Example

Calculate the shaded area in cm² between the two circles shown below.

Give your answer to 3 significant figures.

Answer

Area of outer circle = π x 9² = 81π 

Area of inner circle = π x 8² = 64π 

Shaded area = 81π - 64π = 17π = 53.38 cm² 

= 53.4 cm ² (3 s.f.)

Let's have a go at some questions.