Question

Circle A has a radius of 9.0 cm. The shortest distance between B and C on the circle is 8.5 cm. What is the approximate area of the shaded portion of circle A?
30.0 cm²

38.25 cm²

56.5 cm²

254.5 cm²

Answer 1

Answer:

38.25 cm²

Step-by-step explanation:

We use the formula for the length of an arc to find the central angle of the sector of the circle.

Then we use the formula for the area of a sector of a circle to find the area.

Length of arc of circle of radius r:

$s = \dfrac{n}{360^\circ}2 \pi r$

s = arc length

n = measure of the central angle of the sector

$s = \dfrac{n}{360^\circ}2 \pi r$

$8.5~cm = \dfrac{n}{360^\circ}2 \pi \times 9.0~cm$

$n = 54.1^\circ$

Area of sector of circle of radius r:

$A = \dfrac{n}{360^\circ} \pi r^2$

A = area of sector of circle

n = measure of the central angle of the sector

$A = \dfrac{54.1^\circ}{360^\circ} \pi (9.0~cm)^2$

$A= 38.25~cm^2$