Question

Trina has $1000 to purchase an open-top cylindrical dog pen in her backyard. She wants the height of the pen to be 5 feet. If the pen costs $1 per square foot, what is the biggest pen (in terms of the radius) that she can afford? Round your answer to the nearest hundredth of a foot.

Answer 1

The largest radius would be 31.85 feet.

We want the area around the cylinder.  This is a rectangle whose length is the circumference of the circle and the width is the height.

C = πd = 2πr

The area would then be
A=2πrh

Since each foot of fence is $1, and she can afford $1000, she can get at most 1000 feet of fence;

1000 = 2(3.14)(r)(5)
1000 = 31.4r

Divide both sides by 31.4:
1000/31.4 = 31.4r/31.4
31.85 = r