The formula for the surface area of a sphere is 4πr2

Question

. 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.