Chapter 11, Problem 20MCQ

To determine

To find: The area covered by $8$ sections.

Answer to Problem 20MCQ

The area of the sector is $50.88c{m}^2$ .

Explanation of Solution

Given Information: Given diameter is $9\mathrm{cm}$ and each orange has $10$ congruent sections.

Given diameter is $9\mathrm{cm}$ and each orange has $10$ congruent sections.

Central angle $=\frac{{360}^{\circ }}{10}={36}^{\circ }$ .

Radius $=\frac{9}{2}=4.5\mathrm{cm}$ .

Area of each sector:

  $\begin{array}{l}=\frac{\theta }{{360}^{\circ }}\pi r^2\\ =\frac{{36}^{\circ }\times 22\times 4.5\times 4.5}{{360}^{\circ }\times 7}\\ =6.36{\mathrm{cm}}^2\end{array}$

Area of $8$ sector $=8\times 6.36=50.88c{m}^2$ .

Thus, the area of the $8$ sector is $50.88c{m}^2$ .