An open rectangular cistern when measured from outside is 1.35 m long, 1.08 m broad and 90 cm deep. It is made up of iron, which is 2.5 cm thick. Find the capacity of the cistern and the volume of the iron used.

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Solution

External length of the cistern = 1.35 m = 135 cm
External breadth of the cistern = 1.08 m = 108 m
External height of the cistern = 90 cm
∴ External volume of the cistern $= 135 \times 108 \times 90 {cm}^{3} = 1312200 {cm}^{3}$

In order to find the internal volume of the cistern, we need to determine the internal dimensions of the cistern.
Internal length of the cistern = 135 − (2.5 + 2.5) cm = 130 cm
Internal breadth of the cistern = 108 − (2.5 + 2.5) = 103 cm [ Subtracting the thickness of iron from both sides ]
Internal height of the cistern = 90 − 2.5 cm = 87.5 cm
∴ Internal volume of the cistern = $= 130 \times 103 \times 87.5 = 1171625 {cm}^{3}$

i.e., capacity of the cistern = 1171625 cm³
∴ Volume of iron used = external volume of the cistern − internal volume of the cistern
= (1312200 − 1171625) cm³ = 140575 cm³

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