# circular pool w/ circumference of 23 ft. Pool is surrounded by a fence 2.5 ft apart from edge of the pool. What is the circumference of the fence?

justaguide | College Teacher | (Level 2) Distinguished Educator

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The radius of the circular pool is 23 feet. Circumference of a circle is given by 2*pi*r

2*pi*r = 23

=> r = 23/(2*pi)

The pool is surrounded by a fence that is 2.5 feet apart.

This increases the radius of the fence by 2.5.

The circumference of the fence is 2*pi*[23/(2*pi)) + 2.5]

=> 5*pi + 23

The circumference of the fence is 23 + 5*pi feet.

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Given the circumference of the pool is 23 feet.

==> C = 2* r * pi

==> 23 = 2*r * pi

==> r= 23/2pi = 3.66 ft

Now we need to determine the circumference of the fence.

We know that the radius is the pool is 3.66

Also, the fence is 2.5 ft from the pool.

Then the radius of the fence is 3.66 + 2.5 = 6.16

Now we will calculate the circumference.

==> C = 2* r * pi = 2* 6.16 * pi = 38.708 ft

Then the circumference of the fence is 38.708 ft.