Question

52 part a which of the following is closest to the circumference, in meters, of the circle? (a) a 18.8 b 37.7 c 59.2 d 113.0 (b) part b what is the area, in square meters, of the circle? a 6π b 12π c 36π d 144π

Explanation:

Part A

Step1: Recall circumference formula

The formula for the circumference of a circle is \( C = 2\pi r \) (or \( C=\pi d \), where \( d \) is diameter). From Part B, the area is \( 36\pi \), and the area formula is \( A=\pi r^{2} \). So, \( \pi r^{2}=36\pi \), which means \( r^{2} = 36 \), so \( r = 6 \) meters (radius).

Step2: Calculate circumference

Using \( C = 2\pi r \), substitute \( r = 6 \): \( C=2\pi\times6=12\pi\approx12\times3.14 = 37.68\approx37.7 \).

The area of a circle is given by the formula \( A=\pi r^{2} \). From the circumference calculation (or by solving the area formula), if we assume we found the radius (from Part A, we saw that when \( A = 36\pi \), \( r^{2}=36 \) so \( r = 6 \)). Then, substituting \( r = 6 \) into the area formula: \( A=\pi\times6^{2}=36\pi \).

Answer:

B. 37.7

Part B