To calculate the surface area of spheres A and B, we can use the formula for the surface area of a sphere, which is:
\[ \text{Surface Area} = 4\pi r^2 \]
Calculating Sphere A:
- Radius \( r = 6 \) in.
\[ \text{Surface Area of Sphere A} = 4\pi (6^2) = 4\pi (36) = 144\pi \text{ in}^2 \]
Calculating Sphere B:
- Radius \( r = 24 \) in.
\[ \text{Surface Area of Sphere B} = 4\pi (24^2) = 4\pi (576) = 2304\pi \text{ in}^2 \]
Comparison of the Surface Areas:
- Surface Area of Sphere A: \( 144\pi \)
- Surface Area of Sphere B: \( 2304\pi \)
To find out how many times larger Sphere B's surface area is compared to Sphere A's surface area, we can use:
\[ \frac{\text{Surface Area of Sphere B}}{\text{Surface Area of Sphere A}} = \frac{2304\pi}{144\pi} = \frac{2304}{144} = 16 \]
This means that Sphere B’s surface area is 16 times as large as Sphere A’s.
So, the correct statement based on the calculations 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.
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