Question

1. crater lake in oregon is shaped like a circle with a diameter of about 5.5 miles.

a. how far is it around the perimeter of crater lake?
b. what is the area of the surface of crater lake?

Explanation:

Part a

Step1: Recall the formula for the circumference of a circle.

The formula for the circumference \( C \) of a circle is \( C = \pi d \), where \( d \) is the diameter.

Step2: Substitute the given diameter into the formula.

Given that the diameter \( d = 5.5 \) miles, we substitute this into the formula: \( C=\pi\times5.5 \approx 3.14\times5.5 = 17.27 \) miles.

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. The radius \( r \) is half of the diameter, so \( r=\frac{d}{2} \).

Step2: Calculate the radius.

Given \( d = 5.5 \) miles, the radius \( r=\frac{5.5}{2}=2.75 \) miles.

Step3: Substitute the radius into the area formula.

Substitute \( r = 2.75 \) into \( A=\pi r^{2} \): \( A=\pi\times(2.75)^{2}\approx3.14\times7.5625 = 23.758125 \) square miles.

Answer:

The distance around (circumference) of Crater Lake is approximately \( 17.27 \) miles.

Part b