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

$A_r=C\times h$

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

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