Proved
See explanation below
Step-by-step explanation:
Surface area of a cylinder = 2πr² + 2πrh
The derivation of formula:
A cylinder comprises of two circles and one rectangle as seen in the net diagram of a cylinder:
The area of one circle = πr²
Area of two circles = 2 × area of one circle
Area of two circles = 2(πr²) = 2πr²
The area of rectangle = length × width
width of the rectangle = smallest side = h
length of the rectangle = longest side
The length of the rectangle is the part that covers the circle at the top and at the bottom.
To determine its value, we would need to calculate the circumference of a circle.
This corresponds to the length of the rectangle in the net diagram
circumference of a circle = 2πr
Area of the rectangle = 2πr × h = 2πrh
The surface area of the cylinder = Area of the two circles + area of the rectangle
The surface area of the cylinder = 2πr² + 2πrh
S = 2πr² + 2πrh
Proved