To calculate the surface area of both spheres, we will use the formula for the surface area of a sphere:
\[ \text{Surface Area} = 4\pi r^2 \]
For Sphere A:
- Radius \( r_A = 6 \) in. \[ \text{Surface Area of Sphere A} = 4\pi (6)^2 = 4\pi (36) = 144\pi \text{ in}^2 \]
For Sphere B:
- Radius \( r_B = 24 \) in. \[ \text{Surface Area of Sphere B} = 4\pi (24)^2 = 4\pi (576) = 2304\pi \text{ in}^2 \]
Now, let's compare the surface areas of the two spheres:
- Surface Area of Sphere A = \( 144\pi \) in²
- Surface Area of Sphere B = \( 2304\pi \) in²
To determine how many times larger Sphere B's surface area is compared to Sphere A's: \[ \frac{\text{Surface Area of Sphere B}}{\text{Surface Area of Sphere A}} = \frac{2304\pi}{144\pi} = \frac{2304}{144} = 16 \]
Thus, Sphere B’s surface area is 16 times as large as Sphere A’s.
Final Conclusion: Sphere A has a surface area of \( 144\pi \) in², and Sphere B has a surface area of \( 2304\pi \) in². This means that Sphere B's surface area is 16 times as large as Sphere A's.
So the correct response is: Sphere A has a surface area of \( 144\pi \) in², and Sphere B has a surface area of \( 2304\pi \) in². This means that Sphere B's surface area is 16 times as large as Sphere A's.
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