Question

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 can use the formula for the surface area of a sphere:

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

**For Sphere A (radius = 3 cm):**

\[
\text{Surface Area of Sphere A} = 4\pi (3)^2
\]
\[
= 4\pi (9)
\]
\[
= 36\pi \text{ cm}^2
\]

**For Sphere B (radius = 6 cm):**

\[
\text{Surface Area of Sphere B} = 4\pi (6)^2
\]
\[
= 4\pi (36)
\]
\[
= 144\pi \text{ cm}^2
\]

Now, we can compare the surface areas of the two spheres:

- Surface Area of Sphere A = \(36\pi\) cm²
- Surface Area of Sphere B = \(144\pi\) cm²

To find out how many times larger the surface area of Sphere B is compared to Sphere A, we divide the surface area of Sphere B by that of Sphere A:

\[
\text{Ratio} = \frac{\text{Surface Area of Sphere B}}{\text{Surface Area of Sphere A}} = \frac{144\pi}{36\pi} = \frac{144}{36} = 4
\]

**Final results:**
- 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.