Question

Garrett wants to make a circular pond in his yard and put a low fence around the edge. What is the largest area pond Garrett can make if he has 136 feet of fencing?

A.
21.66 square feet

B.
468.98 square feet

C.
1472.61 square feet

D.
14,519.36 square feet
Please help, I suck at math -w-

Answer 1

The answer is C. 1472.61 square feet

Explanation:

If you are familiar with Pi (π) you can do a lot of fun stuff with math.

Let's review some values:

A = Area, C = circumference, r = radius, π = 3.14159 (commonly rounded off to 3.14).

You might already know that the area of a circle can be calculated with the formula A = π r2 (pi r squared).

However, we do not know the radius in this instance so this formula isn't going to work for us.

Let's try a different way.

We do know the circumference. The circumference is simply the length of the fencing, 136 feet.

So we'll use this formula:

A = C2 / 4π

C2 is 136 x 136, or 18,496. Don't be scared off by this huge number; we're going to whittle it down.

4π = 12.56

18,496/12.56 (or 18,496 divided by 12.56) = 1472.61

Wasn't that fun?

Answer 2

Option C is the answer.

Explanation:

We have been given that the pond is circular and the measurement of fencing is 136 feet.

In other words we can say that the circumference is 136 feet.

The formula for circumference is =
`2\pi r` where r is the radius of the circle.

So, we get;

`136=2*3.14* r`

=>
`136=6.28r`

`r=(136)/(6.28)`

r = 21.65 feet

Area of the circle is given as =
`\pi r^(2)`

So, the largest area will be =
`3.14*21.65^(2)`

= 1471.79 square feet. (close to 1472.61 or option C)