Find the surface area of a sphere with a diameter of 30 inches. Leave your answer in terms of p

1 answer

To find the surface area of a sphere, you can use the formula:

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

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

First, we need to find the radius from the diameter. The diameter of the sphere is given as 30 inches, so the radius \( r \) is:

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

Now, we can substitute the radius into the surface area formula:

\[ A = 4\pi (15)^2 \]

Calculating \( (15)^2 \):

\[ (15)^2 = 225 \]

Now substituting back into the surface area formula:

\[ A = 4\pi \times 225 \]

Calculating \( 4 \times 225 \):

\[ 4 \times 225 = 900 \]

Thus, the surface area \( A \) in terms of \( \pi \) is:

\[ A = 900\pi \]

The surface area of the sphere is \( \boxed{900\pi} \) square inches.