Question

the radius of a semicircle is 17 inches. what is the semicircles area? round your answer to the nearest hundredth. square inches

Explanation:

Step1: Recall the formula for the area of a full circle

The area of a full circle is given by the formula \( A = \pi r^2 \), where \( r \) is the radius of the circle.

Step2: Determine the area of the semicircle

Since a semicircle is half of a full circle, the area of a semicircle (\( A_{semicircle} \)) is half the area of the full circle. So the formula for the area of a semicircle is \( A_{semicircle} = \frac{1}{2} \pi r^2 \).
We are given that the radius \( r = 17 \) inches. Substitute \( r = 17 \) into the formula:

$$
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$$

Now, calculate the numerical value. Using \( \pi\approx3.14159 \):

$$ A_{semicircle}\approx144.5\times3.14159 $$

$$ A_{semicircle}\approx453.96075 $$

Step3: Round to the nearest hundredth

Rounding \( 453.96075 \) to the nearest hundredth (two decimal places), we look at the third decimal place, which is \( 0 \). Since \( 0<5 \), we don't round up the second decimal place. So the value is approximately \( 453.96 \).

Answer:

\( 453.96 \) square inches