To calculate the surface area of both spheres, we will use the formula for the surface area of a sphere:
\[ \text{Surface Area} = 4\pi R^2 \]
Sphere A (Radius = 2 in)
- Calculate \( R^2 \): \[ R^2 = 2^2 = 4 \]
- Plug it into the surface area formula: \[ \text{Surface Area}_A = 4\pi \times 4 = 16\pi \text{ square inches} \]
Sphere B (Radius = 10 in)
- Calculate \( R^2 \): \[ R^2 = 10^2 = 100 \]
- Plug it into the surface area formula: \[ \text{Surface Area}_B = 4\pi \times 100 = 400\pi \text{ square inches} \]
Comparison
Now let's compare the surface areas of the two spheres:
- Sphere A: \( 16\pi \) square inches
- Sphere B: \( 400\pi \) square inches
To express how they relate to each other, we can calculate the ratio of their surface areas:
\[ \frac{\text{Surface Area}_A}{\text{Surface Area}_B} = \frac{16\pi}{400\pi} = \frac{16}{400} = \frac{1}{25} \]
So, Sphere B has 25 times the surface area of Sphere A.
Final Results
- Surface Area of Sphere A: \( 16\pi \) square inches
- Surface Area of Sphere B: \( 400\pi \) square inches
- Sphere B is 25 times larger in surface area than Sphere A.