Question

Using the figure below, derive a formula to solve the surface area

Answer 1

We have a cylinder and we need to find its surface area

It formed from 2 circles (bases)

The rule of the area of the circle is

`A_C=\pi r^2`

Then the area of the 2 bases is

`A_b=2\pi r^2`

The curved part is formed from a rectangle its length is the circumference of the base and its width is the height of the cylinder, then

`A_r=C* h`

C is the circumference of the circle and h is the height of the cylinder

The rule of the circumference is

`C=2\pi r`

Then the area of the curved part (rectangle) is

`A_r=2\pi rh`

Then the total surface area is the sum of the area of the 2 bases and the rectangle

`C.S.A=2\pi r^2+2\pi rh`