Question

Find the surface area of a sphere with a diameter of 34 meters. Use the symbol for pi. (13 points)
Responses

2,724 m2
2,724 m2

3,632 m2
3,632 m2

3,972 m2
3,972 m2

4,216 m2

Answer 1

To find the surface area of a sphere, we use the formula:

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

where \( r \) is the radius of the sphere. The diameter of the sphere is given as 34 meters, so we can find the radius \( r \) by dividing the diameter by 2:

\[
r = \frac{34}{2} = 17 \text{ meters}
\]

Now, we can substitute the radius into the surface area formula:

\[
\text{Surface Area} = 4\pi (17)^2
\]

Calculating \( (17)^2 \):

\[
(17)^2 = 289
\]

Now we can calculate the surface area:

\[
\text{Surface Area} = 4\pi \times 289 = 1156\pi \text{ m}^2
\]

Now, to find the approximate numerical value of \( 1156\pi \), we can use \( \pi \approx 3.14 \):

\[
1156 \times 3.14 \approx 3637.44 \text{ m}^2
\]

Rounding this value, we can say that the surface area of the sphere is approximately:

\[
\text{Surface Area} \approx 3,632 \text{ m}^2
\]

Therefore, the correct response is:

\[
\boxed{3,632 \text{ m}^2}
\]