To calculate the surface area of each sphere, we will use the formula for the surface area of a sphere:
\[ \text{Surface Area} = 4\pi R^2 \]
Sphere A
- Radius \( R_A = 6 \) inches
\[ \text{Surface Area of Sphere A} = 4\pi (6)^2 = 4\pi \times 36 = 144\pi \ \text{square inches} \]
Sphere B
- Radius \( R_B = 24 \) inches
\[ \text{Surface Area of Sphere B} = 4\pi (24)^2 = 4\pi \times 576 = 2304\pi \ \text{square inches} \]
Comparison
Now, we can compare the surface areas of both spheres:
- Surface Area of Sphere A: \( 144\pi \) square inches
- Surface Area of Sphere B: \( 2304\pi \) square inches
To see how much larger Sphere B is compared to Sphere A, we can calculate the ratio of their surface areas:
\[ \text{Ratio} = \frac{\text{Surface Area of Sphere B}}{\text{Surface Area of Sphere A}} = \frac{2304\pi}{144\pi} = \frac{2304}{144} = 16 \]
Conclusion
Sphere B has a surface area that is 16 times larger than that of Sphere A.
- Surface Area of Sphere A: \( 144\pi \) square inches
- Surface Area of Sphere B: \( 2304\pi \) square inches
- Sphere B's surface area is 16 times that of Sphere A.