Bot GPT 4-o mini To calculate the surface area of each sphere, we will use the formula for the surface area of a sphere:
\[ \text{Surface Area} = 4\pi r^2 \]
For Sphere A (radius = 4 inches):
\[ \text{Surface Area of Sphere A} = 4\pi (4)^2 = 4\pi (16) = 64\pi \text{ in}^2 \]
For Sphere B (radius = 10 inches):
\[ \text{Surface Area of Sphere B} = 4\pi (10)^2 = 4\pi (100) = 400\pi \text{ in}^2 \]
Now, we can compare the surface areas:
\[ \frac{\text{Surface Area of Sphere B}}{\text{Surface Area of Sphere A}} = \frac{400\pi}{64\pi} = \frac{400}{64} = 6.25 \]
Thus, Sphere B's surface area is 6.25 times as large as Sphere A's.
Final Results:
- 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.
So 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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