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.

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

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

Answer 2

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

Too much!

Answer 3

How do you do it?

Answer 4

C = pi * d

C = 3.14 * 64
C = 200.96

Cost = 200.96 * 5 * 1

Cost = 1004.80

Answer 5

To solve this problem, we need to find the maximum radius of the cylindrical dog pen that Trina can afford.

First, let's calculate the surface area of the cylinder. The formula for the surface area of a cylinder is given by the equation:

Surface Area = 2πrh + πr^2

In this case, the height (h) is given as 5 feet. Let's let the radius be represented by r. So the surface area equation becomes:

Surface Area = 2π(5)r + πr^2

Now, Trina has $1000 to spend, and the cost is given as $1 per square foot. So the cost equation becomes:

Cost = $1 x Surface Area

Since the cost should not exceed $1000, we can equate these two equations:

$1 x Surface Area = $1000
2π(5)r + πr^2 = $1000

Simplifying the equation:

10πr + πr^2 = $1000
πr^2 + 10πr - $1000 = 0

Now, we can solve this quadratic equation to find the value of r.

Using the quadratic formula:

r = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = π, b = 10π, and c = -1000.

Plugging these values into the quadratic formula:

r = (-10π ± √((10π)^2 - 4π(-1000))) / (2π)

Simplifying further:

r = (-10π ± √(100π^2 + 4000π)) / (2π)
r = (-10π ± √(100π(π + 40))) / (2π）
r = (-10 ± √(π(π + 40))) / 2

Since we are looking for the maximum radius, we take the positive value:

r = (-10 + √(π(π + 40))) / 2

Calculating this expression, we get:

r ≈ 7.81

Since we need to round to the nearest foot, the biggest pen (in terms of the radius) Trina can afford is approximately 8 feet.

Therefore, the correct answer is A) 8 feet.