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 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 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 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.

Answer 1

To calculate the surface area of the spheres, we can use the formula:

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

For Sphere A:

• Radius (r) = 6 in.
• Surface Area = \( 4\pi (6)^2 \)
• Surface Area = \( 4\pi (36) \)
• Surface Area = \( 144\pi , \text{in}^2 \)

For Sphere B:

• Radius (r) = 24 in.
• Surface Area = \( 4\pi (24)^2 \)
• Surface Area = \( 4\pi (576) \)
• Surface Area = \( 2304\pi , \text{in}^2 \)

Now, let's compare the surface areas of the two spheres:

• Surface Area of Sphere A = \( 144\pi , \text{in}^2 \)
• Surface Area of Sphere B = \( 2304\pi , \text{in}^2 \)

To find out how many times larger the surface area of Sphere B is compared to Sphere A:

\[ \frac{\text{Surface Area of Sphere B}}{\text{Surface Area of Sphere A}} = \frac{2304\pi}{144\pi} = \frac{2304}{144} = 16 \]

Thus, Sphere B's surface area is 16 times larger than Sphere A's.

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.