Cylinder

Cylinder

A cylinder is a solid object having curved surface with two circular faces of same size. Measuring jars, circular pillars, circular pipes, gluesticks etc. are some examples of cylinder. A cylinder is also called a circular prism. The figure given below is a cylinder.

Where,

AX = BY = r = radius of cylinder

AB = XY = h = height of cylinder

XY = axis of cylinder

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If the axis of cylinder is perpendicular to the circular base then the cylinder is called a right circular cylinder, otherwise it is called an oblique cylinder.

Net of right circular cylinder

Net of right circular cylinder is as given below:

Formula for surface area and volume of right circular cylinder

Curved surface area (CSA) of cylinder = 2πrh

Total surface area (TSA) of cylinder = 2πr(r + h)

Volume of cylinder = πr²h

Hollow Cylinder

A hollow cylinder is a solid bounded by two co-axial cylinders of the same height and different radii. For example - water pipe, rubber pipe etc. The figure given below is a hollow cylinder where R is external radius and r is the internal radius.

i.        Area of base ring = πR² – πr² = π(R² – r²)

ii.       Curved surface area of hollow cylinder = External surface + Internal surface

                        = 2πRh + 2πrh

                        = 2πh(R + r)

iii.      Total surface area of hollow cylinder = Curved surface area + 2 Area of base ring

                    = 2πh(R+r) + 2π(R²–r²)

                    = 2πh(R+r) + 2 π(R+r) (R–r)

                    = 2π(R+r) (h+R–r)

iv.      Volume of the material used in hollow cylinder = External volume – internal volume

                         = πR²h – πr²h

                         = πh(R² – r²)

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