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Question

If the area of the below shape is 18π cm2, then the value of r is cm

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Solution

Given shape is a semicircle as it formed by cutting a whole circle along a diameter line.

Here, r is the distance from the center of the semicircle to it's circumference, so r is the radius of the semicircle.

Given, Area of the semicircle =18×π cm2
We know: Area of semicircle =12× Area of the circle
18π=12×πr2
Multiply both sides by 2
18π×2=12×πr2×2
36π=πr2
Divide both sides by π
36ππ=πr2π
36=r2
Taking square root both sides
36=r2
6×6=r2
±6=r
r=6(The radius of a semicircle cannot be negative
r=6 is rejected)

Hence, the the value of r is 6 cm.

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