Question

Sara is cutting circles out of pieces of cardboard. If she uses a rectangular piece of cardboard that is 8 in. 10 in., what is the area of the largest circle she could make?

Answer 1

50.29 square inches.

Explanation:

Given:

Sara is cutting circles out of pieces of cardboard.

She uses a rectangular piece of cardboard that is 8 inches by 10 inches.

Question asked:

What is the area of the largest circle she could make?

Solution:

Here given length of piece of cardboard is 10 inches and breadth is 8 inches, to draw the largest circle, we have to draw the circle touching the boundary of the breadth of the rectangular cardboard and hence breadth will be considered as diameter and it will be the maximum diameter of the circle.

Now, we will find the area of the largest circle by taking breadth as the maximum possible diameter:

Breadth = Diameter = 8 inches ( given )

Radius = half of diameter ,
`r =(d)/(2) =(8)/(2) = 4\ inches`

`Area \ of\ circle =\pi r^(2)`

`=(22)/(7) *4*4\\=(352)/(7) =50.285\ square\ inches`

Therefore, area of the largest circle she could make is 50.29 square inches.