To calculate the surface area of each sphere, we can use the formula for the surface area of a sphere:
\[ \text{Surface Area} = 4\pi R^2 \]
where \( R \) is the radius of the sphere.
For Sphere A:
- Radius (\( R \)) = 3 cm
\[ \text{Surface Area of Sphere A} = 4\pi (3)^2 = 4\pi \cdot 9 = 36\pi , \text{cm}^2 \]
For Sphere B:
- Radius (\( R \)) = 6 cm
\[ \text{Surface Area of Sphere B} = 4\pi (6)^2 = 4\pi \cdot 36 = 144\pi , \text{cm}^2 \]
Comparison of Surface Areas:
- Surface Area of Sphere A: \( 36\pi , \text{cm}^2 \)
- Surface Area of Sphere B: \( 144\pi , \text{cm}^2 \)
To compare their surface areas, we can find the ratio of the surface areas:
\[ \text{Ratio} = \frac{\text{Surface Area of Sphere B}}{\text{Surface Area of Sphere A}} = \frac{144\pi}{36\pi} = \frac{144}{36} = 4 \]
This means that Sphere B has a surface area that is 4 times greater than that of Sphere A.
In conclusion:
- Surface Area of Sphere A = \( 36\pi , \text{cm}^2 \)
- Surface Area of Sphere B = \( 144\pi , \text{cm}^2 \)
- Sphere B's surface area is 4 times larger than Sphere A's surface area.