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:C. 31.83 feet.Step-by-step 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.[tex]\text{Surface area of cylinder}=2\pi rh[/tex],where,r = Radius of cylinder,h = Height of cylinder.[tex]\text{Surface area of cylinder}=2\pi r*5[/tex][tex]\text{Surface area of cylinder}=10\pi r[/tex]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.[tex]1000=10\pi r[/tex]Upon dividing both sides of our equation by 10 pi we will get,[tex]\frac{1000}{10\pi}=\frac{10\pi r}{10\pi}[/tex][tex]31.8309886=r[/tex][tex]r\approx 31.83[/tex]Therefore, the radius of the dog pen is 31.83 feet and option C is the correct choice.