Question

Find the surface area of a cylinder with a diameter of 14 cm and a height of 22 cm.(1 point)
Responses

1,274.84 cm2
1,274.84 cm2

1,230.88 cm2
1,230.88 cm2

3,165.12 cm2
3,165.12 cm2

1,934.24 cm2

Answer 1

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

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

where \( r \) is the radius and \( h \) is the height of the cylinder.

Given:
- Diameter of the cylinder = 14 cm, thus the radius \( r = \frac{14}{2} = 7 \) cm.
- Height \( h = 22 \) cm.

Now, substituting these values into the formula:

1. Calculate the area of the two circular bases:
\[
2\pi r^2 = 2\pi (7)^2 = 2\pi (49) = 98\pi
\]

2. Calculate the lateral surface area:
\[
2\pi rh = 2\pi (7)(22) = 2\pi (154) = 308\pi
\]

3. Combine both areas to get the total surface area:
\[
\text{Surface Area} = 98\pi + 308\pi = 406\pi
\]

Now, we can compute the numerical value using \( \pi \approx 3.14 \):
\[
406\pi \approx 406 \times 3.14 \approx 1274.84 \text{ cm}^2
\]

Thus, the surface area of the cylinder is approximately **1,274.84 cm²**.

The correct response is:
**1,274.84 cm²**