Question

Help this is due tomorrow please! Carter has 88 feet of fencing to enclose a dog pen in his yard. He is trying to decide whether to make the pen circular or square. Assuming he uses all of the fencing, what is the difference between the area of the circular pen and the square pen? ​

Answer 1

Answer:

The circle makes the larger area

The difference in the two areas is roughly 132.2479 square feet.

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Explanation:

If Carter decides to go for a circle, then 88 is the circumference, which is the distance around the circle (aka perimeter of the circle).

Use this to find the radius needed

C = 2*pi*r

r = C/(2pi)

r = 88/(2pi)

r = 44/pi

I'll leave it in exact form rather than approximate it.

Once we know the radius, we can find the area of the circle.

A = pi*r^2

A = pi(44/pi)^2

A = pi*(1936/(pi^2))

A = 1936/pi

A = 616.247939651819 approximately

I used my calculator's stored version of pi to compute the area in the final step.

We'll be comparing this number later, so hold onto it for now.

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If Carter instead decides for a square, then 88 is the perimeter since it's the amount of fencing he has to work with.

Divide it into 4 pieces to find the length of each side of the square (all sides are equal in a square)

88/4 = 22

Each side is 22 feet

The area of this square is (22)^2 = 22*22 = 484 square feet

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Summary:

• If Carter goes for a circular enclosure, then he gets roughly 616.2479 square feet.
• The square enclosure only gets him exactly 484 square feet.

The circle wins in terms of larger area.

The difference being roughly 616.2479  - 484 = 132.2479 square feet.