Question

Surface Area of Cylinders Practice

Answer 1

Sure! To calculate the surface area of a cylinder, you need to know two measurements: the radius (r) of the base and the height (h) of the cylinder.

The formula for the surface area (SA) of a cylinder is:

\[
SA = 2\pi r(h + r)
\]

This formula accounts for the area of the two circular bases and the area of the curved surface.

1. **Area of the two bases**: \( 2\pi r^2 \)
2. **Area of the curved surface**: \( 2\pi rh \)

Putting it all together gives you the total surface area:

\[
SA = 2\pi r^2 + 2\pi rh = 2\pi r(h + r)
\]

### Let's practice with some examples!

**Example 1:**
- Radius (r) = 3 cm
- Height (h) = 5 cm

Calculate the surface area.

**Example 2:**
- Radius (r) = 4 m
- Height (h) = 10 m

Calculate the surface area.

### Solutions:

**Example 1:**
1. Calculate the surface area using the formula:
\[
SA = 2\pi(3)(5 + 3)
\]
\[
SA = 2\pi(3)(8)
\]
\[
SA = 48\pi \approx 150.8 \text{ cm}^2
\]

**Example 2:**
1. Calculate the surface area:
\[
SA = 2\pi(4)(10 + 4)
\]
\[
SA = 2\pi(4)(14)
\]
\[
SA = 112\pi \approx 351.9 \text{ m}^2
\]

Feel free to try your own examples or ask for more practice problems!