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 blank π cm2 . Sphere B has a surface area of blank π cm2 . The surface area of sphere B is blank times larger than the surface area of sphere A . fill in the blanks

Answer 1

To calculate the surface area of each sphere, we will use the formula \( S = 4\pi r^2 \).

**For Sphere A (radius = 3 cm):**
\[
S_A = 4\pi(3^2) = 4\pi(9) = 36\pi \text{ cm}^2
\]

**For Sphere B (radius = 6 cm):**
\[
S_B = 4\pi(6^2) = 4\pi(36) = 144\pi \text{ cm}^2
\]

Now we'll fill in the blanks based on the calculations:

- Sphere A has a surface area of **36** π cm².
- Sphere B has a surface area of **144** π cm².

Next, to compare their surface areas, we calculate how many times larger the surface area of sphere B is compared to that of sphere A:
\[
\text{Comparison} = \frac{S_B}{S_A} = \frac{144\pi}{36\pi} = 4
\]

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

To summarize the filled blanks:

- Sphere A has a surface area of **36** π cm².
- Sphere B has a surface area of **144** π cm².
- The surface area of sphere B is **4** times larger than the surface area of sphere A.