# Cylinder

cylinder is a closed solid that has two parallel (circular) bases connected by a curved surface.

The height h is the perpendicular distance between the bases.

r of a cylinder is the radius of a base.

Pi (π) is the ratio of a circle’s circumference to its diameter (π = c/d). It is a mathematical constant, with a value of 3.14159…

The volume V of a cylinder with radius r is the area of the base times the height h.

or

# V=(π r²) h

The surface area of a cylinder is the number of square units it takes to cover all the surface of a cylinder.

# A = p h + 2 b

p is the perimeter of the circle (equals to 2 π r)

# A=2 π r h + 2 π r²

## Surface Area

If you unroll a cylinder, its net is two circles and a parallelogram.

The area of each circle is   π r².

The area of the parallelogram is (2 π r)(h) = 2 π r h

The surface area of a cylinder with height h and radius r is the area of the two bases plus the area of the curved surface (parallelogram).

# A= 2 (π r²) + (2 π r) h

2 π r  is the perimeter (circumference of the circle), and h  the height of the cylinder.