Question

Find the surface area of a cylinder with a radius of 4 and a height of 3. Use 3.14 for π
top 4 mm
the side 3mm
(1 point)
Responses

709.89 mm2
709.89 mm 2

175.84 mm2
175.84 mm 2

100.48 mm2
100.48 mm 2

75.36 mm2

Answer 1

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

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

where:
- \( r \) is the radius
- \( h \) is the height
- The first term, \( 2\pi r^2 \), represents the area of the two circular bases.
- The second term, \( 2\pi rh \), represents the lateral surface area.

Given:
- Radius \( r = 4 \) mm
- Height \( h = 3 \) mm
- Use \( \pi = 3.14 \)

Now, let's calculate the surface area step by step.

1. Calculate the area of the two bases:
\[
2\pi r^2 = 2 \times 3.14 \times (4)^2 = 2 \times 3.14 \times 16 = 100.48 \text{ mm}^2
\]

2. Calculate the lateral surface area:
\[
2\pi rh = 2 \times 3.14 \times 4 \times 3 = 2 \times 3.14 \times 12 = 75.36 \text{ mm}^2
\]

3. Add both areas together:
\[
\text{Surface Area} = 100.48 + 75.36 = 175.84 \text{ mm}^2
\]

Therefore, the surface area of the cylinder is **175.84 mm²**.