To calculate the surface areas of Sphere A and Sphere B, we can use the formula for the surface area of a sphere:
\[ \text{Surface Area} = 4\pi r^2 \]
Sphere A
- Radius (r): 4 inches
- Surface Area:
\[ \text{Surface Area of Sphere A} = 4\pi (4^2) = 4\pi (16) = 64\pi \text{ in}^2 \]
Sphere B
- Radius (r): 10 inches
- Surface Area:
\[ \text{Surface Area of Sphere B} = 4\pi (10^2) = 4\pi (100) = 400\pi \text{ in}^2 \]
Comparison of Surface Areas
- Surface Area of Sphere A: \( 64\pi \text{ in}^2 \)
- Surface Area of Sphere B: \( 400\pi \text{ in}^2 \)
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 the surface area of Sphere A:
\[ \text{Ratio} = \frac{\text{Surface Area of Sphere B}}{\text{Surface Area of Sphere A}} = \frac{400\pi}{64\pi} = \frac{400}{64} = 6.25 \]
Thus, Sphere B's surface area is 6.25 times as large as Sphere A's.
Conclusion
The correct calculation shows:
- 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.
None of the options A, B, C, or D provided in the initial problem statement correctly represent the calculations. However, the closest is D, which inaccurately states "6.35" instead of the correct "6.25". The correct relationships should be made clear.
1 answer