Question

find the diameter of each circle.

1. area = 4π in² \t\t\t 18) area = 49π yd²

\t 4 in \t\t\t\t\t 14 yd

1. circumference = 162π yd \t 20) circumference =

\t 162 yd \t\t\t\t 30 yd

Explanation:

Problem 17:

Step 1: Recall the area formula of a circle.

The area of a circle is given by \( A = \pi r^2 \), where \( A \) is the area and \( r \) is the radius. We are given \( A = 4\pi \) \( \text{in}^2 \). So we set up the equation:
\( \pi r^2 = 4\pi \)

Step 2: Solve for the radius \( r \).

Divide both sides of the equation by \( \pi \):
\( r^2 = \frac{4\pi}{\pi} = 4 \)
Take the square root of both sides:
\( r = \sqrt{4} = 2 \) \( \text{in} \) (we take the positive root since radius is a positive quantity)

Step 3: Find the diameter \( d \).

The diameter of a circle is related to the radius by the formula \( d = 2r \). Substitute \( r = 2 \) \( \text{in} \):
\( d = 2\times2 = 4 \) \( \text{in} \)

Step 1: Recall the area formula of a circle.

The area of a circle is \( A = \pi r^2 \), with \( A = 49\pi \) \( \text{yd}^2 \). Set up the equation:
\( \pi r^2 = 49\pi \)

Step 2: Solve for the radius \( r \).

Divide both sides by \( \pi \):
\( r^2 = \frac{49\pi}{\pi} = 49 \)
Take the square root:
\( r = \sqrt{49} = 7 \) \( \text{yd} \)

Step 3: Find the diameter \( d \).

Using \( d = 2r \), substitute \( r = 7 \) \( \text{yd} \):
\( d = 2\times7 = 14 \) \( \text{yd} \)

Step 1: Recall the circumference formula of a circle.

The circumference of a circle is given by \( C = \pi d \) (where \( d \) is the diameter) or \( C = 2\pi r \). We are given \( C = 162\pi \) \( \text{yd} \). Using \( C = \pi d \), we set up the equation:
\( \pi d = 162\pi \)

Step 2: Solve for the diameter \( d \).

Divide both sides by \( \pi \):
\( d = \frac{162\pi}{\pi} = 162 \) \( \text{yd} \)

Answer:

The diameter of the circle is \( \boldsymbol{4} \) inches.

Problem 18: