Question

what is the area of a circular region whose diameter is 12 centimeters?
a 36π square cm
b 36π cm
c 12π cm
d 24π square cm

Explanation:

Step1: Find the radius

The diameter \( d = 12 \) cm, and the radius \( r=\frac{d}{2}\). So \( r = \frac{12}{2}=6 \) cm.

Step2: Calculate the area of the circle

The formula for the area of a circle is \( A=\pi r^{2} \). Substitute \( r = 6 \) into the formula: \( A=\pi\times6^{2}=\pi\times36 = 36\pi \) square cm. Also, note that the unit for area should be square centimeters, so options with non - square units (B, C) are incorrect, and D has an incorrect numerical value.

Answer:

A. \( 36\pi \) square cm