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) Responses 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. Sphere upper A has a surface area of 16 pi in. squared and sphere upper B has a surface area of 400 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 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.

Question

GPT-4o mini · Answer

To calculate the surface area of spheres A and B using the formula \( A = 4\pi r^2 \):

For Sphere A (radius \( r = 2 \) in): \[ A_A = 4\pi(2^2) = 4\pi(4) = 16\pi \text{ in}^2 \]
For Sphere B (radius \( r = 10 \) in): \[ A_B = 4\pi(10^2) = 4\pi(100) = 400\pi \text{ in}^2 \]

Now, to compare the surface areas:

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

To find how many times larger Sphere B's surface area is compared to Sphere A's, divide the surface area of Sphere B by that of Sphere A: \[ \frac{A_B}{A_A} = \frac{400\pi}{16\pi} = \frac{400}{16} = 25 \]

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

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.