Question

Round Oak Park has a large circular lake with a walking path around it that is 15 miles long. Find the radius of the lake and approximate area of the lake. Round answers to tenths.

The approximate radius of the lake is
[ Select ]
miles.

The approximate area of the lake is
[ Select ]
square miles.

Answer 1

The circumference of a circle is given by the formula:

C = 2πr

where C is the circumference and r is the radius.

In this problem, we know that the circumference of the lake is 15 miles. So we can set up the following equation:

15 = 2πr

Solving for r, we get:

r = 15 / (2π)

r ≈ 2.4 miles (rounded to the nearest tenth)

So the approximate radius of the lake is 2.4 miles.

The area of a circle is given by the formula:

A = πr^2

where A is the area and r is the radius.

Using the radius we just found, we can calculate the approximate area of the lake:

A = π(2.4)^2

A ≈ 18.1 square miles (rounded to the nearest tenth)

Therefore, the approximate area of the lake is 18.1 square miles.