Question

The formula for the surface area of a sphere is 4πr^2. Sphere A has a radius of 3 cm and sphere B has a radius 6 cm. Calculate the surface area of each sphere and compare their surface areas.

Sphere A has a surface area of __ π cm^2. Sphere B has a surface area of __ π cm^2. 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, which is \( 4\pi r^2 \).

**For Sphere A:**
- Radius \( r = 3 \) cm
- Surface Area \( A_A = 4\pi (3)^2 = 4\pi (9) = 36\pi \) cm²

**For Sphere B:**
- Radius \( r = 6 \) cm
- Surface Area \( A_B = 4\pi (6)^2 = 4\pi (36) = 144\pi \) cm²

**Comparison:**
To find how many times larger the surface area of sphere B is compared to sphere A:
\[
\frac{A_B}{A_A} = \frac{144\pi}{36\pi} = \frac{144}{36} = 4
\]

So, we have:
- 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.

Thus, the final answers are:
- 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.