Area of shaded part inside the circle

Geometry Level 1

The radius of the circle shown is 8 meters. Find the area of the shaded part in square meters. Use $\pi=3.14$ .

155.186 square meters 155.168 square meters 155.816 square meters 155.681 square meters

2 solutions

Hana Wehbi
Dec 25, 2019

Nice problem.

Thanks. It is an original problem.

A Former Brilliant Member - 1 year, 5 months ago

Richard Desper
Dec 23, 2019

Use the fact that an inscribed angle of $t$ degrees cuts an arc of $2t$ degrees. Thus the arc cut by the $17^\circ$ angle has measure of $34^\circ$ , and the arc cut by the $24^\circ$ angle has measure of $48^\circ$ . The white sector thus spans $82^\circ$ , leaving $278^\circ$ degrees of the circle in the gray area.

Thus the are of the gray sector is $\frac{278}{360}*64 \pi \approx 155.1858$ when we use the approximation $\pi \approx 3.14$ .

Area of shaded part inside the circle

2 solutions

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