Question

A Circle fits inside a semicircle of radium 28mm

Answer 1

`147\pi \: {mm}^(2)`

Explanation:

If the diameter of the semicircle is 28 mm, that means its radius is half diameter:

`r(semicircle) = 0.5 * 28 = 14 \: mm`

The radius of the semicircle is equal to the diameter of the smaller circle

The radius of the smaller circle is also half diameter:

`r(smaller \: circle) = 0.5 * 14 = 7 \: mm`

Now, we can find the area of the smaller circle:

`a(smaller \: circle) = \pi * {r}^(2) = \pi * {7}^(2) = 49\pi \: {mm}^(2)`

We also have to find the area of the semicircle in order to find the area of the shaded area:

`a(semicircle) = \pi * {r}^(2) =\pi * {14}^(2) = 196\pi \: {mm}^(2)`

Now, let's subtract the area of the circle from the area of the semicircle and we'll have the answer:

`a(shaded \: area) = 196\pi - 49 \pi = 147\pi \: {mm}^(2)`