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 4πr2 .(1 point)

Question

Responses

Sphere A has a surface area of 4π in.2 and sphere B has a surface area of 100π in.2, meaning sphere B’s surface area is 25 times as large as sphere A’s.
Sphere upper A has a surface area of 4 pi in. squared and sphere upper B has a surface area of 100 pi in. squared , meaning sphere upper B ’s surface area is 25 times as large as sphere upper A ’s.

Sphere A has a surface area of 2π in.2 and sphere B has a surface area of 10π in.2, meaning sphere B’s surface area is 4 times as large as sphere A’s.
Sphere upper A has a surface area of 2 pi in. squared and sphere upper B has a surface area of 10 pi in. squared , meaning sphere upper B ’s surface area is 4 times as large as sphere upper A ’s.

Sphere A has a surface area of 8π in.2 and sphere B has a surface area of 40π in.2, meaning sphere B’s surface area is 5 times as large as sphere A’s.
Sphere upper A has a surface area of 8 pi in. squared and sphere upper B has a surface area of 40 pi in. squared , meaning sphere upper B ’s surface area is 5 times as large as sphere upper A ’s.

Sphere A has a surface area of 16π in.2 and sphere B has a surface area of 400π in.2, meaning sphere B’s surface area is 25 times as large as sphere A’s.

Answer 1

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

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

For Sphere A:

• Radius \( r = 2 \) in.
• Surface Area = \( 4\pi (2^2) = 4\pi (4) = 16\pi \) in²

For Sphere B:

• Radius \( r = 10 \) in.
• Surface Area = \( 4\pi (10^2) = 4\pi (100) = 400\pi \) in²

Comparison of Surface Areas:

• Sphere A has a surface area of \( 16\pi \) in².
• Sphere B has a surface area of \( 400\pi \) in².

To find out how many times larger sphere B's surface area is compared to sphere A's surface area, we can divide the two areas:

\[ \frac{400\pi}{16\pi} = \frac{400}{16} = 25 \]

Thus, sphere B's surface area is 25 times as large as sphere A's.

Therefore, the correct response is:

"Sphere A has a surface area of 16π in.² and sphere B has a surface area of 400π in.², meaning sphere B’s surface area is 25 times as large as sphere A’s."