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 10 in. The formula for the surface area of a sphere is 47p2
• (1 point)

Answer 1

It looks like there's a small typo in the formula you've provided for the surface area of a sphere. The correct formula for the surface area \( S \) of a sphere is:

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

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

### For Sphere A:
- Radius \( r_A = 2 \) in
- Surface Area \( S_A \) is calculated as follows:

\[
S_A = 4\pi (2)^2 = 4\pi \times 4 = 16\pi \text{ in}^2
\]

### For Sphere B:
- Radius \( r_B = 10 \) in
- Surface Area \( S_B \) is calculated as follows:

\[
S_B = 4\pi (10)^2 = 4\pi \times 100 = 400\pi \text{ in}^2
\]

### Comparison:
Now we can compare the surface areas of the two spheres:

- Sphere A Surface Area: \( 16\pi \text{ in}^2 \)
- Sphere B Surface Area: \( 400\pi \text{ in}^2 \)

To compare the two values, we can look at the ratio of their surface areas:

\[
\text{Ratio} = \frac{S_B}{S_A} = \frac{400\pi}{16\pi} = \frac{400}{16} = 25
\]

Thus, the surface area of Sphere B is 25 times that of Sphere A.

### Summary:
- Surface area of Sphere A: \( 16\pi \text{ in}^2 \)
- Surface area of Sphere B: \( 400\pi \text{ in}^2 \)
- Sphere B has a surface area 25 times greater than that of Sphere A.