Question

question 17 of 44
what is the area of the circle shown below?
image of a circle with center c and radius 22 cm

a. 138.2 cm²
b. 1520.5 cm²
c. 6082.1 cm²
d. 69.1 cm²

Explanation:

Step1: Recall the formula for the area of a circle

The formula for the area \( A \) of a circle is \( A=\pi r^{2} \), where \( r \) is the radius of the circle.

Step2: Identify the radius of the circle

From the diagram, the radius \( r = 22\space\text{cm}\).

Step3: Substitute the radius into the formula

Substitute \( r = 22 \) into the formula \( A=\pi r^{2} \). We get \( A=\pi\times(22)^{2} \).
First, calculate \( 22^{2}=22\times22 = 484 \). Then, \( A=\pi\times484 \). Taking \( \pi\approx3.1416 \), we have \( A\approx3.1416\times484 \).
Calculate \( 3.1416\times484 = 3.1416\times(400 + 80+4)=3.1416\times400+3.1416\times80 + 3.1416\times4=1256.64+251.328+12.5664 = 1520.5344\approx1520.5\space\text{cm}^2 \)

Answer:

B. \( 1520.5\space\text{cm}^2 \)