Question

the radius of a semicircle is 3 yards. what is the semicircles area?
r=3 yd
round your answer to the nearest hundredth.
square yards

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, \( A_{semicircle} = \frac{1}{2} \pi r^2 \).
We are given that the radius \( r = 3 \) yards. Substitute \( r = 3 \) into the formula:
\( A_{semicircle} = \frac{1}{2} \times \pi \times (3)^2 \)
First, calculate \( (3)^2 = 9 \). Then, \( \frac{1}{2} \times \pi \times 9 = \frac{9\pi}{2} \).

Step3: Calculate the numerical value and round

Using \( \pi \approx 3.14159 \), we have \( \frac{9 \times 3.14159}{2} = \frac{28.27431}{2} = 14.137155 \).
Rounding this to the nearest hundredth (two decimal places), we look at the third decimal place, which is 7. Since 7 > 5, we round up the second decimal place. So, 14.137155 rounded to the nearest hundredth is 14.14.

Answer:

14.14