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. A) 7.96 feet B) 15.92 feet C) 31.83 feet D) 63.66 feet

Answer 1

C. 31.83 feet.

Explanation:

We have been given that 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.

First of all, we will find the surface area of dog pen using surface area of cylinder.

`\text{Surface area of cylinder}=2\pi rh`,where,

r = Radius of cylinder,

h = Height of cylinder.

`\text{Surface area of cylinder}=2\pi r*5`

`\text{Surface area of cylinder}=10\pi r`

Since the area of each square foot of pen costs $1, so in $1000 Trina can cover an area of 1000 square feet.

Now, we will set the surface area of cylinder equal to 1000 to solve for the radius.

`1000=10\pi r`

Upon dividing both sides of our equation by 10 pi we will get,

`(1000)/(10\pi)=(10\pi r)/(10\pi)`

`31.8309886=r`

`r\approx 31.83`

Therefore, the radius of the dog pen is 31.83 feet and option C is the correct choice.