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.

V = B 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 b + (perimeter) h

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.

A= 2 π r² + 2 π r h

 SA09 Cylinder

SA10 Cylinder

SA11 Cylinder

SA12 Cylinder

 

VO28 Cylinder Problems