Similar Figures and Surface Area Quick Check

Question

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 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.
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 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.

Answer 1

To solve the problem, we will use the formula for the surface area of a sphere, which is \( S = 4\pi r^2 \).

For Sphere A:

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

For Sphere B:

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

Comparison of Surface Areas:

Now we will compare the surface areas of both spheres:

• \( S_A = 144\pi , \text{in}^2 \)
• \( S_B = 2304\pi , \text{in}^2 \)

To find how many times larger sphere B's surface area is compared to sphere A's, we calculate:

\[ \frac{S_B}{S_A} = \frac{2304\pi}{144\pi} = \frac{2304}{144} = 16 \]

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

Conclusion:

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.