Question

1. what is the diameter of a circle whose area is 314 square meters?

a. 10 meters
b. 20 meters

Explanation:

Step1: Recall the area formula of a circle

The area of a circle is given by the formula \( A=\pi r^{2} \), where \( A \) is the area and \( r \) is the radius. We know that \( A = 314 \) square meters and we can use \( \pi\approx3.14 \). So we substitute the values into the formula: \( 314 = 3.14\times r^{2} \).

Step2: Solve for the radius \( r \)

First, divide both sides of the equation \( 314 = 3.14\times r^{2} \) by \( 3.14 \). So \( \frac{314}{3.14}=r^{2} \), which simplifies to \( 100 = r^{2} \). Then, take the square root of both sides. Since \( r>0 \) (radius is a positive quantity), we have \( r = \sqrt{100}=10 \) meters.

Step3: Find the diameter \( d \)

The diameter of a circle is related to the radius by the formula \( d = 2r \). We found that \( r = 10 \) meters, so \( d=2\times10 = 20 \) meters.

Answer:

b. 20 meters