Volume of a Cylinder

Volume of a Cylinder

The space covered by a solid cylinder is known as the volume of that cylinder.  Volume of a cylinder is given by the product of its area of circular base (πr²) and the height (h) of the cylinder.

i.e. Volume of cylinder = Area of the circular base × height

                                    = πr² × h

                                    = πr²h

∴  Volume of the cylinder = πr²h

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Volume of material of a 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. 

Let R be the external radius and r be the internal radius of a hollow cylinder as given in the figure below. Then,

The volume of the material of hollow cylinder = External volume – internal volume

                                                                        = πR²h – πr²h

                  = πh(R² – r²)

Workout Examples

Example 1: Find volume of the cylinder:

Solution: Here,

                          Diameter of the cylinder (d) = 14cm

                          ∴  Radius of the cylinder (r) = 14cm/2 = 7cm

                          Height of the cylinder (h) = 20cm

                We know,

                                Volume of cylinder (V) = πr²h

                                                                       = 22/7 × 7² × 20

                                                                       = 22 × 7 × 20

                                                                       = 3080cm³

                Thus, the volume of cylinder is 3080cm³.

Example 2: The volume of a cylinder is 770cm³. If the height of the cylinder is 5cm, find the radius of the base of cylinder.

Solution: Here,

                           Height of the cylinder (h) = 5cm.

                           Volume of cylinder = 770cm³

                i.e.      πr²h = 770

                or,      22/7 × r² × 5 = 770

                or,      110/7 × r² = 770

                or,      r² = 770 × 7/110

                or,      r² = 7²

                or,      r = 7cm

                Thus, the radius of the base of cylinder is 7cm.

Example 3: The sum of the height and the radius of a cylinder is 37cm. If the area of total surface is 1628cm³, find the volume of the cylinder.

Solution: Here,

                           r + h = 37cm ……………….. (i)

                           Total surface area (TSA) of cylinder = 1628cm³

     i.e.      2πr(r + h)  = 1628

                or,      2 × 22/7 × r × 37 = 1628

                or,      1628/7 × r = 1628

                or,      r = 1628 × 7/1628

                or,      r = 7cm

                Putting the value of r in (i),

                           7 + h = 37

                or,      h = 37 – 7

                or,      h = 30cm

                Now,

                          Volume of cylinder = πr²h

                                                           = 22/7 × 7² × 30

                                                           = 4620cm³

                Thus, the volume of cylinder is 4620cm³.

Example 4: In the adjoining figure, the internal and external radii of the metallic pipe are 3cm and 4cm respectively. If the length of the pipe is 35cm, find the volume of the metal.

Solution: Here,

                           The internal radius of the pipe (r) = 3cm.

                           The external radius of the pipe (R) = 4cm

                           The height (or length) of the pipe (h) = 35cm

                Now,

                           The volume of the metal = πh(R² – r²)

                                                                     = 22/7 × 35 × (4² – 3²)

                                                                     = 22 × 5 × (16 – 9)

                                                                     = 110 × 7

                                                                     = 770cm³

                Thus, the volume of the metal in the pipe is 770cm³.

You can comment your questions or problems regarding the volume and surface area of cylinders here.