Finding Area word problem

Question

How many square feet are in the largest circle that can be cut from a piece of carpet 10 yards by 7 yards?

Answer 1

A diameter of 7 indicates a radius of 3.5 so the area of the circle is pi(3.5) square = 12.5 pi

Answer 2

A circle has a constant diameter. The "largest circle" is the one with the largest diameter. Using a rectangular piece of carpet that is 10 ydx x 7 yds, the largest diameter is 7 yds.

"square feet" is an area.

The area of a circle is Πr².

Now, since Π does not have an exact decimal representation, we approximate it using 3.14. And, since 1/00th of a foot is difficult enough to measure when cutting carpet, that is a "close enough" answer.

However, this problem uses a "magic number" (that is 7) because a less accurate approximation of Π is 22/7 (note: use this concept when accuracy of answer allows it).

A = (22/7)*(7)²

A = 22*7

A = 154 ft²

Note that if you used Π=3.14, you would get A=153.86 ft². With carpet, you would have a very difficult time cutting 7/50ths of a square foot.