Similar Figures and Surface Area Quick Check 1 of 51 of 5 Items Question Calculate and compare the surface area of sphere A , which has a radius of 6 in., and sphere B , which has a radius of 24 in. The formula for the surface area of a sphere is 4πr2 .(1 point) Responses Sphere A has a surface area of 6π in.2 and sphere B has a surface area of 24π in.2. This means that sphere B’s surface area is 4 times as large as sphere A’s. Sphere upper A has a surface area of 6 pi in. squared and sphere upper B has a surface area of 24 pi in. squared . This means that sphere upper B ’s surface area is 4 times as large as sphere upper A ’s. Sphere A has a surface area of 144π in.2 and sphere B has a surface area of 2,304π in.2. This means that sphere B’s surface area is 16 times as large as sphere A’s. Sphere upper A has a surface area of 144 pi in. squared and sphere upper B has a surface area of 2,304 pi in. squared . This means that sphere upper B ’s surface area is 16 times as large as sphere upper A ’s. Sphere A has a surface area of 36π in.2 and sphere B has a surface area of 576π in.2. This means that sphere B’s surface area is 16 times as large as sphere A’s. Sphere upper A has a surface area of 36 pi in. squared and sphere upper B has a surface area of 576 pi in. squared . This means that sphere upper B ’s surface area is 16 times as large as sphere upper A ’s. Sphere A has a surface area of 24π in.2 and sphere B has a surface area of 96π in.2. This means that sphere B’s surface area is 4 times as large as sphere A’s. Sphere upper A has a surface area of 24 pi in. squared and sphere upper B has a surface area of 96 pi in. squared . This means that sphere upper B ’s surface area is 4 times as large as sphere upper A ’s. Skip to navigation page 17 of 17 Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.

Answer 1

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

1. Sphere A (radius = 6 in): \[ S_A = 4\pi(6^2) = 4\pi(36) = 144\pi \text{ in}^2 \]

2. Sphere B (radius = 24 in): \[ S_B = 4\pi(24^2) = 4\pi(576) = 2304\pi \text{ in}^2 \]

Now, to compare the surface areas:

• The surface area of sphere A is \( 144\pi \text{ in}^2 \).
• The surface area of sphere B is \( 2304\pi \text{ in}^2 \).

To find out how many times larger sphere B's surface area is than sphere A's, divide the surface area of sphere B by the surface area of sphere A: \[ \frac{S_B}{S_A} = \frac{2304\pi}{144\pi} = \frac{2304}{144} = 16 \]

Thus, sphere B's surface area is 16 times as large as sphere A's.

Final Answer:

Sphere A has a surface area of \( 144\pi \text{ in}^2 \), and sphere B has a surface area of \( 2304\pi \text{ in}^2 \). This means that sphere B’s surface area is 16 times as large as sphere A’s.

The correct response is: Sphere A has a surface area of 144π in.² and sphere B has a surface area of 2,304π in.². This means that sphere B’s surface area is 16 times as large as sphere A’s.