Question

from unit 3, lesson 10
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 circumference formula

The formula for the circumference \( C \) of a circle is \( C=\pi d \), where \( d \) is the diameter. Here, \( d = 5.5 \) miles.

Step2: Calculate circumference

Substitute \( d = 5.5 \) into the formula: \( C=\pi\times5.5\approx3.14\times5.5 = 17.27 \) miles.

Part b

Step1: Find radius from diameter

The radius \( r \) is half of the diameter, so \( r=\frac{d}{2}=\frac{5.5}{2}=2.75 \) miles.

Step2: Recall area formula for circle

The area \( A \) of a circle is \( A = \pi r^{2} \).

Step3: Calculate area

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

Answer:

s:
a. Approximately \( 17.27 \) miles.
b. Approximately \( 23.76 \) square miles (rounded to two decimal places).