Chapter 11.8, Problem 28PPS

To determine

To find the distance around the semicircle and its area.

Answer to Problem 28PPS

Distance around semicircle $=20.6$ millimeters and area of semicircle $=25.1$ square millimeters.

Explanation of Solution

Given information: Diameter $d=8$ millimeters

Formula used: Distance around semicircle $s=\frac{\pi \times d}{2}+d$ and area $a=\frac{\pi \times r^2}{2}$

Calculation: Distance of semicircle

  $s=\frac{\pi \times d}{2}+d$

Putting in the values of ‘d’.

  $=\frac{22}{7}\times \frac{8}{2}+8$

Taken $\pi =\frac{22}{7}$ .

  $=20.57$

Rounding to the nearest tenth.

  $=20.6$ millimeters

Area of semicircle $a=\frac{\pi \times r^2}{2}$

Here, $r=\frac{d}{2}$

  $=\frac{8}{2}$

  $=4$ millimeters

Area $a=\frac{\pi \times r^2}{2}$

  $=\frac{22\times 4^2}{7\times 2}$

Taken ‘pi’ as $\frac{22}{7}$

  $=\frac{22\times 16}{14}$

On simplifying the expression

  $=25.14$

Rounding to the nearest tenth.

  $=25.1$ square millimeters.