To calculate the surface area of both spheres, we will use the formula for the surface area of a sphere:
\[ \text{Surface Area} = 4\pi r^2 \]
For Sphere A (radius = 6 in.):
\[ \text{Surface Area}_A = 4\pi (6)^2 \]
Calculating \( (6)^2 \):
\[ (6)^2 = 36 \]
Now substituting back into the equation:
\[ \text{Surface Area}_A = 4\pi (36) = 144\pi \]
So, Sphere A has a surface area of \( 144\pi , \text{in}^2 \).
For Sphere B (radius = 24 in.):
\[ \text{Surface Area}_B = 4\pi (24)^2 \]
Calculating \( (24)^2 \):
\[ (24)^2 = 576 \]
Now substituting back into the equation:
\[ \text{Surface Area}_B = 4\pi (576) = 2304\pi \]
So, Sphere B has a surface area of \( 2304\pi , \text{in}^2 \).
Comparison:
Now, let's compare the surface areas of Sphere A and Sphere B:
- Surface Area of Sphere A: \( 144\pi , \text{in}^2 \)
- Surface Area of Sphere B: \( 2304\pi , \text{in}^2 \)
To determine how many times larger Sphere B's surface area is compared to that of Sphere A, divide the surface area of Sphere B by that of Sphere A:
\[ \frac{2304\pi}{144\pi} = \frac{2304}{144} = 16 \]
Thus, Sphere B’s surface area is 16 times larger than Sphere A's surface area.
Final Results:
- Sphere A has a surface area of \( 144\pi , \text{in}^2 \).
- Sphere B has a surface area of \( 2304\pi , \text{in}^2 \).
- Sphere B's surface area is 16 times larger than Sphere A's surface area.