To find the surface area of each sphere, we can use the formula for the surface area of a sphere:
\[ \text{Surface Area} = 4\pi r^2 \]
Calculating the surface area for Sphere A:
- Radius \( r_A = 3 \) cm \[ \text{Surface Area of Sphere A} = 4\pi (3)^2 = 4\pi (9) = 36\pi , \text{cm}^2 \]
Calculating the surface area for Sphere B:
- Radius \( r_B = 6 \) cm \[ \text{Surface Area of Sphere B} = 4\pi (6)^2 = 4\pi (36) = 144\pi , \text{cm}^2 \]
Summary of results:
- Sphere A has a surface area of \( 36\pi \) cm².
- Sphere B has a surface area of \( 144\pi \) cm².
Comparing the surface areas: To find out how many times larger the surface area of Sphere B is compared to Sphere A, we can divide the surface area of Sphere B by the surface area of Sphere A:
\[ \text{Ratio} = \frac{\text{Surface Area of Sphere B}}{\text{Surface Area of Sphere A}} = \frac{144\pi}{36\pi} = \frac{144}{36} = 4 \]
Thus, Sphere B's surface area is 4 times larger than that of Sphere A.
Final answers:
- Sphere A has a surface area of \( 36\pi \) cm².
- Sphere B has a surface area of \( 144\pi \) cm².
- The surface area of Sphere B is 4 times larger than the surface area of Sphere A.
1 answer