Question

If a semicircle's area is 50% in², how long is its radius?

A) 40 inches
B) 30 inches
C) 20 inches
D) 10 inches​ ​

Answer 1

D

Explanation:

Given :

⇒ Area = 50π in²

Formula :

Area (Semicircle) = 1/2 × πr²

Solving :

⇒ 50π = 1/2 × πr²

⇒ r² = 50π/π × 2

⇒ r² = 100

⇒ r = 10 inches

Answer 2

Option D - 10 inches

Explanation:

Area of of a circle is given by the formula :

A = πr²

Area of a semicircle is given by the formula :

A = 1/2×πr²

Now we substitute our area value to solve for r :

50π = 1/2πr²

Multiply both sides by 2 :

100π = πr²

Divide both sides by π :

100 = r²

Square root both sides :

√100 = r

10 = r

Therefore our answer is option D of 10 inches

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