To calculate the surface area of the two spheres using the formula for the surface area of a sphere, \( S = 4\pi r^2 \), we can plug in the radii for each sphere.
For Sphere A:
- Radius \( r_A = 6 \) in. \[ S_A = 4\pi (6)^2 \] \[ S_A = 4\pi (36) \] \[ S_A = 144\pi , \text{in}^2 \]
For Sphere B:
- Radius \( r_B = 24 \) in. \[ S_B = 4\pi (24)^2 \] \[ S_B = 4\pi (576) \] \[ S_B = 2304\pi , \text{in}^2 \]
Comparison of Surface Areas:
Now we compare the surface areas:
- Sphere A: \( 144\pi , \text{in}^2 \)
- Sphere B: \( 2304\pi , \text{in}^2 \)
To find out how many times larger the surface area of sphere B is compared to sphere A: \[ \text{Ratio} = \frac{S_B}{S_A} = \frac{2304\pi}{144\pi} = \frac{2304}{144} = 16 \]
Conclusion:
Sphere A has a surface area of \( 144\pi , \text{in}^2 \), and sphere B has a surface area of \( 2304\pi , \text{in}^2 \). This means that sphere B’s surface area is 16 times as large as sphere A’s.
The correct response is: Sphere A has a surface area of 144π in.² and sphere B has a surface area of 2,304π in.². This means that sphere B’s surface area is 16 times as large as sphere A’s.