Question

Mike is purchasing fabric for a school project. He needs to cut out circles with an area of 314 square inches. The fabric at the store is precut into squares, each of which has a whole number of inches for the length of its side. What is the smallest square piece of fabric Mike can purchase to use to cut out one of the circles?

Answer 1

20 inches

Explanation:

Mike needs to cut out circles with an area of 314 square inches.

Let d be the diameter of required the circle,

So, the area of the circle
`=(\pi d^2)/(4)`

`\Rightarrow 314 = (\pi d^2)/(4)` [ given]

`\Rightarrow 314* 4 =\pi d^2`

`\Rightarrow 314* 4 =3.14 * d^2` [ using \pi=3.14]

`\Rightarrow d^2=(314* 4)/(3.14)`

`\Rightarrow d^2=400`

`\Rightarrow |d|=√(400)=20`

`\Rightarrow d=\pm 20` inches

Neglecting the negative sign as the length of diameter can't be negative.

So, the diameter of the required circle is
`d=20` inches.

As the available fabric at the store is in the square shape for which length and width are the same, to cut out one circle of diameter
`d`, the dimension of the square must be greater than or equal to
`d`.

So, the length of the smallest square piece of the fabric Mike can purchase to use to cut out one of the circles is
`d=20` inches.