A water tank is of cuboidal shape having length 15 m and breadth 12 m. The sum of the area of the floor and ceiling of the tank is same as the area of four walls of the tank. How many liters of rainwater can be collected in this tank?
1200 × 103 liters
Let the height of the cuboidal tank be \(h\) metres, with length \(l = 15\) m and breadth \(b = 12\) m.
Area of floor + area of ceiling \(= 2lb = 2 \times 15 \times 12 = 360 \text{ m}^2\).
Area of four walls \(= 2h(l+b) = 2h(15+12) = 54h \text{ m}^2\).
Given the two are equal: \(360 = 54h \Rightarrow h = \frac{360}{54} = \frac{20}{3} \text{ m}\).
Volume of the tank \(= l \times b \times h = 15 \times 12 \times \frac{20}{3} = \frac{3600}{3} = 1200 \text{ m}^3\).
Since 1 m³ = 1000 litres, capacity \(= 1200 \times 1000 = 1200 \times 10^{3}\) litres.
Hence, the tank can collect \(1200 \times 10^{3}\) litres of rainwater.
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