Question

the radius of a semicircle is 1 inch. what is the semicircles area? round your answer to the nearest hundredth.

Explanation:

Step1: Recall full circle area formula

The area of a full circle is $A_{full} = \pi r^2$, where $r=1$ inch.

Step2: Calculate semicircle area

A semicircle is half the full circle, so $A_{semi} = \frac{1}{2} \pi r^2$. Substitute $r=1$:
$A_{semi} = \frac{1}{2} \pi (1)^2 = \frac{\pi}{2}$

Step3: Compute and round value

Calculate the decimal value: $\frac{\pi}{2} \approx \frac{3.1416}{2} = 1.5708$, then round to the nearest hundredth.

Answer:

1.57 square inches