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 use the formula for the surface area of a sphere:

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

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

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

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

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

Now we have:

- Sphere A has a surface area of \( 36\pi \) cm².
- Sphere B has a surface area of \( 144\pi \) cm².

To compare their surface areas, we calculate how many times larger the surface area of sphere B is compared to sphere A:

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

Thus, the surface area of sphere B is **4 times larger** than the surface area of sphere A.

To summarize:

- 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 that of sphere A.