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

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.

,where,

r = Radius of cylinder,

h = Height of cylinder.

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.

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

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

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4