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Surface Areas And Volumes — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsSurface Areas And Volumes2 Marks
Question
A rectangular tank 15m long and 11m broad is required to receive entire liquid contents from a fully cylindrical tank of internal diameter 21m and length 5m. Find the least height of the tank that will serve the purpose.
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Answer

Suppose height of the rectangular tank is equal to h.
Length of the tank = 15m
Breadth of the tank = 11m
Further,
length of cylindrical tank = 5m
Radius of cylindrical tank $=\frac{21}{2}\text{m}$
To find out the least height of the tank, equate the volumes of two tanks.
$15\times11\times\text{h}\times\pi\Big(\frac{21}{2}\Big)^2\times5$
$\Rightarrow\text{h}=\frac{22}{7}\times\frac{21}{2}\times\frac{21}{2}\times\frac{5}{15}\times\frac{1}{11}$
$\Rightarrow\text{h}=\frac{21}{2}$
$\Rightarrow\text{h}=10.5$
Hence, the least height of the tank is equal to 10.5

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