Question

calculate and compare the surface area of sphere A, which has a radius of 2 in., and sphere B, which has a radius of 10in. The formula for the surface area of a sphere is 4piR^2

Answer 1

To calculate the surface area of both spheres, we will use the formula for the surface area of a sphere:

\[
\text{Surface Area} = 4\pi R^2
\]

### Sphere A (Radius = 2 in)
1. Calculate \( R^2 \):
\[
R^2 = 2^2 = 4
\]
2. Plug it into the surface area formula:
\[
\text{Surface Area}_A = 4\pi \times 4 = 16\pi \text{ square inches}
\]

### Sphere B (Radius = 10 in)
1. Calculate \( R^2 \):
\[
R^2 = 10^2 = 100
\]
2. Plug it into the surface area formula:
\[
\text{Surface Area}_B = 4\pi \times 100 = 400\pi \text{ square inches}
\]

### Comparison
Now let's compare the surface areas of the two spheres:
- Sphere A: \( 16\pi \) square inches
- Sphere B: \( 400\pi \) square inches

To express how they relate to each other, we can calculate the ratio of their surface areas:

\[
\frac{\text{Surface Area}_A}{\text{Surface Area}_B} = \frac{16\pi}{400\pi} = \frac{16}{400} = \frac{1}{25}
\]

So, Sphere B has 25 times the surface area of Sphere A.

### Final Results
- Surface Area of Sphere A: \( 16\pi \) square inches
- Surface Area of Sphere B: \( 400\pi \) square inches
- Sphere B is 25 times larger in surface area than Sphere A.