Chapter 11.8, Problem 30PPS

To determine

To calculate the distance around the semicircle and its area.

Answer to Problem 30PPS

Distance around quarter circle $=17.9$ inches and area of quarter circle $=19.6$ square inches.

Explanation of Solution

Given information: Radius $r=5$ inches

Formula used: Distance around quarter circle $s=\frac{\pi \times r}{2}+2r$ and area $a=\frac{\pi \times r^2}{4}$

Calculation: Distance of quarter circle $s=\frac{\pi \times r}{2}+2r$

Putting the values in the same.

  $=\frac{\pi \times 5}{2}+2\times 5$

Simplifying the expression.

  $=\frac{22\times 5}{7\times 2}+10$

Taken ‘pi’ as $\frac{22}{7}$

  $=17.86$

Rounding to the nearest tenth.

  $=17.9$ inches

Area of quarter circle $a=\frac{\pi \times r^2}{4}$

Putting the values in the formula.

  $=\frac{22\times 5\times 5}{7\times 4}$

Taken ‘pi’ as $\frac{22}{7}$

  $=19.64$

Rounding to the nearest tenth.

  $=19.6$ square inches.