find the volume of material in pipe length 7 cm if, Circle, Mathematics (O-Level)

Question:Find the volume of material in pipe of length 7 cm, if the internal and external radii are 3 cm and 4 cm (Take `pi` to be `22/7`).

Answer The volume of the larger cylinder

                   = `pi(4)^2` 7 c`m^3`= `pi xx16 xx 7 cm^3`= 112`pi cm^3`.

The volume of the smaller cylinder

                   = `pi(3)^2` 7 c`m^3`= 63`pi cm^3`

The volume of the material
                   = (`112 pi - 63 pi` ) `cm^3`

                   = 49`pi cm^3`

                   = 49`xx 22/7 cm^3`.

                   = 154 `cm^3`.

+ ExplanationNot ModeratedThe volume of material in a pipe:
To find the volume of material in a pipe, which is the volume between two cylinders, subtract the volume of the smaller cylinder from that of the larger.
If the height of the cylinder is h, and the external radius is R, the volume of the larger cylinder= `pi R^2`h.
If the internal radius is r, the volume of the smaller cylinder is `pi r^2`h.
The volume of material in the pipe = `pi R^2`h - `pi r^2`h
                                   = `pi`h(`R^2 - r^2`).

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Find the volume of material in pipe of length 7 cm, if the internal and external radii are 3 cm and 4 cm (Take `pi` to be `22/7`).

Question:Find the volume of material in pipe of length 7 cm, if the internal and external radii are 3 cm and 4 cm (Take `pi` to be `22/7`).

Answer The volume of the larger cylinder = `pi(4)^2` 7 c`m^3`= `pi xx16 xx 7 cm^3`= 112`pi cm^3`. The volume of the smaller cylinder = `pi(3)^2` 7 c`m^3`= 63`pi cm^3` The volume of the material = (`112 pi - 63 pi` ) `cm^3` = 49`pi cm^3` = 49`xx 22/7 cm^3`. = 154 `cm^3`.