To find the surface area of each sphere, we will use the formula for the surface area of a sphere, \( S = 4\pi r^2 \), where \( r \) is the radius of the sphere.
Calculating Sphere A:
- Radius of sphere A, \( r_A = 6 \) inches
- Surface area of sphere A:
\[ S_A = 4\pi (6^2) = 4\pi (36) = 144\pi , \text{in}^2 \]
Calculating Sphere B:
- Radius of sphere B, \( r_B = 24 \) inches
- Surface area of sphere B:
\[ S_B = 4\pi (24^2) = 4\pi (576) = 2304\pi , \text{in}^2 \]
Now we have:
- Surface area of sphere A is \( 144\pi , \text{in}^2 \)
- Surface area of sphere B is \( 2304\pi , \text{in}^2 \)
Next, we can compare the surface areas of the two spheres:
- To find how many times larger the surface area of sphere B is in comparison to sphere A, we divide the surface area of sphere B by the surface area of sphere A:
\[ \text{Ratio} = \frac{S_B}{S_A} = \frac{2304\pi}{144\pi} = \frac{2304}{144} = 16 \]
Thus, sphere B's surface area is 16 times as large as sphere A's.
Therefore, the correct comparison is: Sphere A has a surface area of \( 144\pi , \text{in}^2 \) and sphere B has a surface area of \( 2304\pi , \text{in}^2 \). This means that sphere B's surface area is 16 times as large as sphere A's.
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