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.
- Area of the two bases: \( 2\pi r^2 \)
- 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:
- 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:
- 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!