How to find the area of a cylinder?
Understand the Problem
The question is asking for the method to calculate the surface area of a cylinder. This involves using the formula that takes into account the radius of the circular bases and the height of the cylinder.
Answer
$2\pi r (r + h)$
Answer for screen readers
The final answer is $2\pi r (r + h)$
Steps to Solve
- Identify the formula for the surface area of a cylinder
The total surface area $A$ of a cylinder can be found using the formula: [ A = 2\pi r (r + h) ] where $r$ is the radius of the base of the cylinder and $h$ is the height of the cylinder.
- Calculate the area of the two circular bases
Each base of the cylinder is a circle, and the area $A_{base}$ of one circle is: [ A_{base} = \pi r^2 ] Since there are two bases: [ A_{bases} = 2 \pi r^2 ]
- Calculate the lateral surface area
The lateral surface area $A_{lateral}$ is the area of the rectangle that wraps around the side of the cylinder. The length of this rectangle is the circumference of the base (which is $2\pi r$) and the width is the height $h$ of the cylinder: [ A_{lateral} = 2 \pi r h ]
- Sum the areas of the bases and the lateral surface
Add the area of the two circular bases and the lateral surface area to find the total surface area $A$: [ A = 2 \pi r^2 + 2 \pi r h ] This simplifies to: [ A = 2\pi r (r + h) ]
The final answer is $2\pi r (r + h)$
More Information
The surface area formula for a cylinder considers both its circular bases and the lateral side, providing a complete measure of its exterior surface.
Tips
A common mistake is to forget to include either the lateral surface area or the areas of the circular bases in the total surface area calculation. Make sure to add both contributions to get the correct result.