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 foot.

A) 8 feet
B)16 feet
C)32 feet
D)64 feet


Is it c?

Answer 1

A 32-foot radius would cost her $1,005.

Too much!

Answer 2

How do you do it?

Answer 3

C = pi * d
C = 3.14 * 64
C = 200.96

Cost = 200.96 * 5 * 1

Cost = 1004.80

Answer 4

surface area of the pen
= 2πrh
= 2πr(5) = 10πr square feet
but each square foot costs $1
so cost = 10πr

10πr = 1000
r = 1000/(10π) = appr 31.8 ft

They should not have rounded 31.8 up to 32 ft, since at 32 ft, the cost would have been
2π(32)(5) = $1005.31 and he only has $1000 to spend
but it looks like 32 is the answer they would accept