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The figure shows two semicircles. Find the area of the shaded part in terms of pi. Please explain in detail thank you!

The figure shows two semicircles. Find the area of the shaded part in terms of pi-example-1

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Answer: 3pi/2

This is equivalent to 1.5pi

The units for the area are in square centimeters.

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Work Shown:

The larger semicircle has radius 2 cm.

So r = 2 is plugged into the area of a semicircle formula below

A = (pi*r^2)/2

A = (pi*2^2)/2

A = (4pi)/2

A = 2pi

The area of the larger semicircle is 2pi square cm.

Repeat those steps but now use r = 1. This will compute the area of the unshaded smaller semicircle

A = (pi*r^2)/2

A = (pi*1^2)/2

A = pi/2

The area of the smaller unshaded semicircle is pi/2 square cm.

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From here, we subtract the two results to get the shaded area:

(larger semicircle area) - (smaller semicircle area) = (2pi) - (pi/2) = 3pi/2

This is equivalent to 1.5pi since 3/2 = 1.5

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