Final answer:
To determine the maximum radius of a spherical plushy from a piece of fabric with an area of 171.9 sq. in., the area formula for a circle is used. The calculated radius is approximately 7.4 inches, so the closest available option without exceeding the area is 6.9 inches.
Step-by-step explanation:
The question is asking us to determine the maximum radius of a basketball plushy that can be made from a piece of fabric with an area of 171.9 square inches. To find the maximum radius, we will assume the basketball plushy is spherical, and we use the formula for the area of a circle, since the fabric will need to cover the largest cross-section of the sphere, which is a circle with radius 'r':
A = πr^2
Given the fabric's area, A = 171.9 sq. in., we solve for 'r' as follows:
πr^2 = 171.9
r^2 = 171.9 / π
r = √(171.9 / π)
r ≈ √(54.73)
r ≈ 7.4 inches
Since the options provided are 13.7 in, 6.9 in, 3.7 in, 3.4 in, the closest option without exceeding the available fabric area is option (b) 6.9 in, which corresponds to a diameter of 13.8 in, and an area of approximately 150.72 sq. in. if we use the diameter to calculate the area (π * 6.9^2).