Question

Calculate the area shaded.
To three decimal places

Answer 1

`\approx 116 \: {cm}^(2)`

Explanation:

Radius of the internal circle
`r_1=2.3 \: cm`

Radius of the external circle
`r_2=6.5 \: cm`

Area of the shaded region = Area of external circle - Area of internal circle.

`= \pi r_(2)^(2) - \pi r_(1)^(2) \\ \\ = \pi \{ r_(2)^(2) - r_(1)^(2) \} \\ \\ = \pi \{ (6.5)^(2) - (2.3)^(2) \}\\ \\ = 3.14\{ (6.5 + 2.3) (6.5 - 2.3) \}\\ \\ = 3.14\{8.8 * 4.2 \}\\ \\ = 116.0544 \\ \\ \approx 116 \: {cm}^(2)`