To calculate the surface area of the spheres, we use the formula:
\[ \text{Surface Area} = 4\pi r^2 \]
For Sphere A:
- Radius \( r_A = 6 , \text{in} \)
\[ \text{Surface Area of Sphere A} = 4\pi (6)^2 = 4\pi (36) = 144\pi , \text{in}^2 \]
For Sphere B:
- Radius \( r_B = 24 , \text{in} \)
\[ \text{Surface Area of Sphere B} = 4\pi (24)^2 = 4\pi (576) = 2304\pi , \text{in}^2 \]
Now, we compare the surface areas of the two spheres:
- Sphere A: \( 144\pi , \text{in}^2 \)
- Sphere B: \( 2304\pi , \text{in}^2 \)
To find out how many times larger Sphere B's surface area is compared to Sphere A's, we can divide the surface area of Sphere B by that 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 surface area.
Conclusion: The correct answer is:
C. 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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