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Surface Areas And Volumes — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsSurface Areas And Volumes3 Marks
Question
Water flows through a cylindrical pipe, whose inner radius is $1\ cm$, at the rate of $80\ cm/sec$ in an empty cylindrical tank, the radius of whose base is $40\ cm$.
What is the rise of water level in tank in half an hour?
✓

Answer

Given, radius of tank, $r_1 = 40\ cm$
Let height of water level in tank in half an hour $= h_1$​​​​​​​
Also, given internal radius of cylindrical pipe, $r_1 = 1\ cm$
and speed of water $= 80\ cm/s$ in $1$ water flow $= 80\ cm$
$\therefore$ In $30$ (min) water flow $= 80 \times 60 \times 30 = 144000\ cm$
According to the question,
Volume of water in cylindrical tank = Volume of water flow the circular pipe in half an hour
$\Rightarrow\pi\text{r}^2_1\text{h}_1=\pi\text{r}^2_1\text{h}_2$
$\Rightarrow40\times40\times\text{h}_1=1\times144000$
$\therefore\text{h}_1=\Big(\frac{144000}{40\text{x}40}\Big)=90\text{cm}$
Hence, the level of water in cylindrical tank rises $90\ cm$ in half an hour.

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