The formula for the surface area of a sphere is 4πr2 . Sphere A has a radius of 3 cm and sphere B has a radius of 6 cm. Calculate the surface area of each sphere and compare their surface areas.(2 points) Sphere A has a surface area of π cm2 . Sphere B has a surface area of π cm2 . The surface area of sphere B is times larger than the surface area of sphere A .

Answer 1

To calculate the surface area of each sphere, we will use the formula for the surface area of a sphere:

\[ \text{Surface Area} = 4\pi r^2 \]

For Sphere A:

• Radius (\(r_A\)) = 3 cm
• Surface Area of Sphere A:

\[ \text{Surface Area}_A = 4\pi (3)^2 = 4\pi \cdot 9 = 36\pi \text{ cm}^2 \]

For Sphere B:

• Radius (\(r_B\)) = 6 cm
• Surface Area of Sphere B:

\[ \text{Surface Area}_B = 4\pi (6)^2 = 4\pi \cdot 36 = 144\pi \text{ cm}^2 \]

Comparison of Surface Areas:

Now we compare the surface areas of the two spheres.

To find out how many times larger the surface area of Sphere B is compared to Sphere A, we can use the following calculation:

\[ \text{Factor} = \frac{\text{Surface Area}_B}{\text{Surface Area}_A} = \frac{144\pi}{36\pi} = \frac{144}{36} = 4 \]

Conclusion:

• Surface Area of Sphere A: \(36\pi \text{ cm}^2\)
• Surface Area of Sphere B: \(144\pi \text{ cm}^2\)
• The surface area of Sphere B is 4 times larger than the surface area of Sphere A.