Question

Calculate the area of a segment of a circle with a central angle of $165$ degrees and a radius of $4$. Express answer to nearest integer.

• A. $10$
• B. $20$
• C. $30$
• D. $40$

Answer 1

Answer: (B)

$20$

$A_{segment}=A_{sector}-A_{triangle}$
$A_{sector}=\frac{n}{360}\pi r^2$
$=\frac{165}{360}\pi 4^2$
= 23.02 $c{m}^2$
$A_{triangle}=\frac{1}{2}bh$
b = $2\sqrt{3}$
h = 2
$A_{triangle}=\frac{1}{2}bh$
= $\frac{1}{2}2\sqrt{3}\times 2$
= $3.46$
$A_{segment}=23.02-3.46\approx 20$