Question

mathematics 20 - 3
now, unwrap the cylinder to see its net:
what information do we need to find the surface area of the cylinder? the net has two equal circles and a rectangular section, so sa = 2a_cr+a_r

Explanation:

Step1: Recall circle - area formula

The area of a circle $A_{cr}=\pi r^{2}$, where $r$ is the radius of the circle.

Step2: Recall rectangle - area formula

The area of the rectangle $A_{re}=l\times w$. In the case of the cylinder net, $l = h$ (height of the cylinder) and $w = 2\pi r$ (circumference of the circle), so $A_{re}=2\pi r h$.

Step3: Substitute into surface - area formula

Substitute $A_{cr}=\pi r^{2}$ and $A_{re}=2\pi r h$ into $SA = 2A_{cr}+A_{re}$. We get $SA=2\pi r^{2}+2\pi r h$.

Answer:

We need the radius $r$ of the base - circles and the height $h$ of the cylinder to find its surface area, and the surface - area formula is $SA = 2\pi r^{2}+2\pi r h$.