Calculate and compare the surface area of sphere A

Question

, 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 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.

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.

Answer 1

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

1. For Sphere A:

   • Radius \( r = 6 \) in.
   • Surface Area \( = 4\pi (6)^2 = 4\pi (36) = 144\pi \) in².

2. For Sphere B:

   • Radius \( r = 24 \) in.
   • Surface Area \( = 4\pi (24)^2 = 4\pi (576) = 2304\pi \) in².

Now, let's compare the surface areas:

• Sphere A has a surface area of \( 144\pi \) in².
• Sphere B has a surface area of \( 2304\pi \) in².

To find out how many times larger Sphere B's surface area is compared to Sphere A's: \[ \frac{2304\pi}{144\pi} = \frac{2304}{144} = 16. \]

Thus, Sphere B’s surface area is 16 times as large as Sphere A’s.

Therefore, the correct response is: Sphere A has a surface area of 144π in² and sphere B has a surface area of 2,304π in². This means that sphere B’s surface area is 16 times as large as sphere A’s.