math conexus surface area of cylinders quick check

1 answer

To calculate the surface area of a cylinder, you need to know its radius (r) and height (h). The formula for the surface area (SA) of a cylinder is:

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

This formula consists of two parts:

  1. The lateral (or curved) surface area: \(2\pi rh\)
  2. The area of the two circular bases: \(2\pi r^2\)

So, if you add those two parts together, you arrive at the total surface area formula provided above.

Steps to Calculate the Surface Area of a Cylinder:

  1. Identify the radius (r) and height (h) of the cylinder.
  2. Use the formula: \[ SA = 2\pi r(h + r) \]
  3. Plug in the values for r and h.
  4. Calculate the surface area.

Quick Example:

If a cylinder has a radius of 3 units and a height of 5 units, the surface area would be:

  1. \( r = 3 \), \( h = 5 \)
  2. Plugging into the formula: \[ SA = 2\pi (3)(5) + 2\pi (3^2) \] Which simplifies to: \[ SA = 30\pi + 18\pi = 48\pi \]
  3. Approximately \( 48 \times 3.14 \approx 150.72 \) square units.

Feel free to ask if you have a specific problem or example to work through!