Question

Jonna is sewing a front cover for a circular pillow. The pillow has a diameter of 15 inches. To sew the front cover, she must cut the fabric two inches wider than the pillow all the way around. What is the minimum area, in square inches, of the piece of fabric she will use?

Answer 1

Explanation:

To determine the minimum area of the piece of fabric Jonna needs, we need to calculate the diameter of the circle after adding 2 inches to the radius.

The radius of the pillow is half its diameter, which is 15/2 = 7.5 inches.

When Jonna adds 2 inches to the radius, the new radius becomes 7.5 + 2 = 9.5 inches.

The diameter of the circle with the new radius is 2 x 9.5 = 19 inches.

Therefore, Jonna needs to cut a circular piece of fabric with a diameter of 19 inches.

To calculate the minimum area of the fabric, we need to use the formula for the area of a circle:

Area = π x (radius)^2

The radius is 9.5 inches, so:

Area = π x (9.5)^2

Area = π x 90.25

Area ≈ 283.77 square inches

Therefore, Jonna needs a piece of fabric with a minimum area of approximately 283.77 square inches.