To calculate the surface area of Sphere A and Sphere B, we can use the formula for the surface area of a sphere:
\[ SA = 4\pi r^2 \]
Surface Area of Sphere A (radius = 4 inches)
\[ SA_A = 4\pi (4^2) = 4\pi (16) = 64\pi \text{ in}^2 \]
Surface Area of Sphere B (radius = 10 inches)
\[ SA_B = 4\pi (10^2) = 4\pi (100) = 400\pi \text{ in}^2 \]
Comparing the Surface Areas
Now, we can compare the surface areas of the two spheres:
\[ \frac{SA_B}{SA_A} = \frac{400\pi}{64\pi} = \frac{400}{64} = 6.25 \]
So, Sphere B's surface area is 6.25 times as large as Sphere A's.
Conclusion
Sphere A has a surface area of \(64\pi \text{ in}^2\) and Sphere B has a surface area of \(400\pi \text{ in}^2\), meaning Sphere B's surface area is 6.25 times as large as Sphere A's.
Thus, 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.