To calculate the surface area of a baseball with a 3-inch diameter, follow these steps:
1. Understand the basic formula:
The surface area [tex]\(A\)[/tex] of a sphere is given by the formula:
[tex]\[
A = 4\pi r^2
\][/tex]
where [tex]\(r\)[/tex] 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:
[tex]\[
r = \frac{\text{diameter}}{2} = \frac{3}{2} = 1.5 \text{ inches}
\][/tex]
3. Substitute the radius into the formula:
Plug the radius [tex]\(r = 1.5\)[/tex] inches into the surface area formula:
[tex]\[
A = 4\pi (1.5)^2
\][/tex]
4. Calculate the radius squared:
[tex]\[
(1.5)^2 = 2.25
\][/tex]
5. Multiply by [tex]\(4\pi\)[/tex]:
[tex]\[
A = 4\pi \times 2.25 = 9\pi
\][/tex]
6. Approximate using [tex]\(\pi \approx 3.14\)[/tex]:
[tex]\[
A = 9 \times 3.14 = 28.26 \text{ square inches}
\][/tex]
So, the surface area of the baseball is approximately [tex]\(28.26\)[/tex] 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
