Question

What’s the area of the shaded portion?

The radius of the smallest circle is 4 cm. Each concentric circle has a radius 2 cm than the previous. Find the area of the shaded portion.

Answer 1

`44pi` sq cm

Explanation:

The smallest circle (with a radius of 4 cm) is shaded, so we would need to find the area of that and add it to the other shaded portion.

Area of a circle: `pir^2`

`pi*4^2`

`16pi`

The other shaded portion can be calculated by subtracting the area of the second smallest circle (radius of 6 cm, added on from the 4 cm of the smallest circle) from the second largest circle (radius of 8 cm) since the shaded portion is the part that the second largest circle includes that is not covered by the second smallest circle.

Second largest circle area:

`pi*8^2`

`64pi`

Second smallest circle area:

`pi*6^2`

`36pi`

Subtract:

`64pi-36pi=28pi`

Add that to the smallest circle's area:

`28pi+16pi=44pi`

If you are allowed to leave your answer in terms of pi, then 44pi would be your final answer. Otherwise, multiply 44 by whatever approximation of pi you have been instructed to use (such as 3.14 or 3.14159).