To calculate the surface area of both spheres, we will use the correct formula for the surface area of a sphere, which is:
\[ SA = 4\pi r^2 \]
where \( r \) is the radius of the sphere.
For Sphere A (radius = 6 in):
\[ SA_A = 4\pi (6)^2 = 4\pi (36) = 144\pi \] Using \(\pi \approx 3.14\): \[ SA_A \approx 144 \times 3.14 \approx 452.16 \text{ in}^2 \]
For Sphere B (radius = 24 in):
\[ SA_B = 4\pi (24)^2 = 4\pi (576) = 2304\pi \] Using \(\pi \approx 3.14\): \[ SA_B \approx 2304 \times 3.14 \approx 7238.96 \text{ in}^2 \]
Comparison:
Now we can see how the surface areas compare:
- Sphere A surface area: \( 144\pi \approx 452.16 \text{ in}^2 \)
- Sphere B surface area: \( 2304\pi \approx 7238.96 \text{ in}^2 \)
To find how many times larger Sphere B's surface area is compared to Sphere A's, we divide the two surface areas:
\[ \frac{SA_B}{SA_A} = \frac{2304\pi}{144\pi} = \frac{2304}{144} = 16 \]
This means sphere B's surface area is 16 times as large as sphere A's surface area.
Conclusion:
The correct analysis is:
- Sphere A has a surface area of \( 144\pi \text{ in}^2 \) (approximately \( 452.16 \text{ in}^2 \)).
- Sphere B has a surface area of \( 2304\pi \text{ in}^2 \) (approximately \( 7238.96 \text{ in}^2 \)).
- Sphere B's surface area is 16 times as large as sphere A's.
Thus, the second statement you provided is correct: "Sphere A has a surface area of 144 in² and sphere B has a surface area of 2,304 in². This means that sphere B's surface area is 16 times as large as sphere A's."