Question

Kieran is making a birthday card with construction paper. He wants to cut a circle out of a square piece of construction paper. The circle will have a radius of 6 inches. In square inches, what is the area of the smallest piece of construction paper Kieran could use?

Answer 1

when cutting a circle from a square piece of paper, to use the minimum piece of square paper, midpoints of the edges of the square should be touching the edges of the circle.
For this the length of the square paper should be equal to the diameter of the circle.
If so the the area of the square piece of paper needed;
area = length * length
length of the square = diameter of the circle
diameter = 2 radii
= 2 * 6 inches
= 12 inches
Therefore length of square = 12 inches
area of the square = 12 inches * 12 inches
= 144 sq.inches