To calculate the surface area of spheres A and B, we will use the formula for the surface area of a sphere:
\[ \text{Surface Area} = 4\pi r^2 \]
For Sphere A:
- Radius \( r_A = 4 , \text{in} \)
\[ \text{Surface Area of Sphere A} = 4\pi (4^2) = 4\pi (16) = 64\pi , \text{in}^2 \]
For Sphere B:
- Radius \( r_B = 10 , \text{in} \)
\[ \text{Surface Area of Sphere B} = 4\pi (10^2) = 4\pi (100) = 400\pi , \text{in}^2 \]
Comparison of Surface Areas:
Now, to compare their surface areas, we need to find out how many times the surface area of sphere B is larger than that of sphere A:
\[ \text{Ratio} = \frac{\text{Surface Area of Sphere B}}{\text{Surface Area of Sphere A}} = \frac{400\pi}{64\pi} = \frac{400}{64} = 6.25 \]
Conclusion:
- Sphere A has a surface area of \( 64\pi , \text{in}^2 \).
- Sphere B has a surface area of \( 400\pi , \text{in}^2 \).
- Sphere B's surface area is 6.25 times as large as sphere A's.
Therefore, the correct response is:
Sphere A has a surface area of 64π in² and sphere B has a surface area of 400π in², meaning sphere B's surface area is 6.25 times as large as sphere A's.
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