Question

the radius of a semicircle is 2 centimeters. what is the semicircles area? round your answer to the nearest hundredth. square centimeters

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 formula for the area of a 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, \( A_{semicircle} = \frac{1}{2} \pi r^2 \).

Step3: Substitute the given radius into the formula

We are given that the radius \( r = 2 \) cm. Substituting \( r = 2 \) into the formula for the area of a semicircle, we get:
\( A_{semicircle} = \frac{1}{2} \pi (2)^2 \)

Step4: Simplify the expression

First, calculate \( (2)^2 = 4 \). Then, multiply by \( \frac{1}{2} \) and \( \pi \):
\( A_{semicircle} = \frac{1}{2} \pi \times 4 = 2\pi \)

Step5: Calculate the numerical value and round to the nearest hundredth

Using \( \pi \approx 3.14159 \), we have \( 2\pi \approx 2 \times 3.14159 = 6.28318 \). Rounding this to the nearest hundredth gives \( 6.28 \).

Answer:

The area of the semicircle is approximately \( 6.28 \) square centimeters.