To calculate the surface area of a baseball with a 3-inch diameter, follow these steps:
1. Understand the basic formula:
The surface area \(\(A\)\) of a sphere is given by the formula:
\(\[
A = 4\pi r^2
\]\)
where \(\(r\)\) is the radius of the sphere.
2. Determine the radius:
The diameter of the baseball is given as 3 inches. The radius is half of the diameter:
\(\[
r = \frac{\text{diameter}}{2} = \frac{3}{2} = 1.5 \text{ inches}
\]\)
3. Substitute the radius into the formula:
Plug the radius \(\(r = 1.5\)\) inches into the surface area formula:
\(\[
A = 4\pi (1.5)^2
\]\)
4. Calculate the radius squared:
\(\[
(1.5)^2 = 2.25
\]\)
5. Multiply by \(\(4\pi\)\):
\(\[
A = 4\pi \times 2.25 = 9\pi
\]\)
6. Approximate using \(\(\pi \approx 3.14\)\):
\(\[
A = 9 \times 3.14 = 28.26 \text{ square inches}
\]\)
So, the surface area of the baseball is approximately \(\(28.26\)\) square inches.
Considering the closest option among the given choices:
a) 18.84 in²
b) 53.48 in²
c) 28.3 in²
d) 113.04 in²
The correct answer is:
c) 28.3 in²
