Bonnie is making a circular banner for her youth group. She is cutting the banner out of a square piece of cloth. The banner will have a circumference of 15.7 ft. In order to waste the least amount of material, how many square feet of cloth must Bonnie purchase?

Answer: Bonnie must purchase 25 square feet of cloth.

Step-by-step explanation:

In order to waste the least amount of material, the length of each side of the square piece of cloth must be equal to the diameter of the circular banner that she wants to cut out. The formula for determining the circumference of a circle is expressed as

Circumference = πd

Where

d represents the diameter of the circle

π is a constant whose value is 3.14

Since banner will have a circumference of 15.7 ft, then

3.14d = 15.7

d = 15.7/3.14

d = 5 ft

Area of the square cloth needed is

5² = 25 square feet