Find the surface area of a sphere with a diameter of 30 inches. Leave your answer in terms of pi.(1 point)

Question

Responses

2,826π in.2
2
,
826
𝜋

in.
2
2,826 pi inches squared

225π in.2
225
𝜋

in.
2
225 pi inches squared

3,600π in.2
3
,
600
𝜋

in.
2
3,600 pi inches squared

900π in.2
900
𝜋

in
.
2
900 pi inches squared

Answer 1

The surface area \( A \) of a sphere can be calculated using the formula:

\[ A = 4\pi r^2 \]

where \( r \) is the radius of the sphere.

The diameter of the sphere is given as 30 inches, so the radius \( r \) is half of the diameter:

\[ r = \frac{30}{2} = 15 \text{ inches} \]

Now, plug the radius into the surface area formula:

\[ A = 4\pi (15)^2 \] \[ A = 4\pi (225) \] \[ A = 900\pi \text{ in}^2 \]

Thus, the surface area of the sphere is:

\[ \boxed{900\pi} \text{ in}^2 \]