To calculate and compare the surface area of the two spheres, we will use the formula for the surface area of a sphere, which is:
\[ \text{Surface Area} = 4\pi r^2 \]
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Sphere A:
- Radius \( r = 2 \) in.
- Surface Area \( = 4\pi(2^2) = 4\pi(4) = 16\pi \) in².
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Sphere B:
- Radius \( r = 10 \) in.
- Surface Area \( = 4\pi(10^2) = 4\pi(100) = 400\pi \) in².
Now, let's compare the surface areas:
- Sphere A has a surface area of \( 16\pi \) in².
- Sphere B has a surface area of \( 400\pi \) in².
To find out how many times larger Sphere B’s surface area is compared to Sphere A’s surface area, we can divide the two surface area values:
\[ \frac{400\pi}{16\pi} = \frac{400}{16} = 25 \]
Thus, Sphere B's surface area is 25 times as large as Sphere A’s.
Therefore, the correct response is:
Sphere A has a surface area of \( 16\pi \) in.² and sphere B has a surface area of \( 400\pi \) in.², meaning sphere B’s surface area is 25 times as large as sphere A’s.