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Mensuration - III (Surface Area and Volume of a Right Circular Cylinder) — Maths STD 8 — Question

Maharashtra BoardEnglish MediumSTD 8MathsMensuration - III (Surface Area and Volume of a Right Circular Cylinder)4 Marks
Question
Water flows out through a circular pipe whose internal diameter is 2cm, at the rate of 6 metres per second into a cylindrical tank, the radius of whose base is 60cm. Find the rise in the level of water in 30 minutes?
✓

Answer

Radius of the circular pipe = 0.01m
Length of the water column in 1sec = 6m
Volume of the water flowing in 1s
$=\pi\text{r}^2\text{h}=\pi(0.01)^2(6)\text{m}^3$
Volume of the water flowing in 30 mins
$=\pi(0.01)^2(6)\times 30\times 60\text{m}^3$
Let h m be the rise in the level of water in the cylindrical tank.
Volume of the cylindrical tank in which water is being flown
$=\pi(0.6)^2\times \text{h}$
Volume of water flowing in 30 mins = Volume of the cylindrical tank in which water is being flown.
$\pi(0.01)^2(6)\times30\times60=\pi(0.6)^2\times \text{h}$
$\text{h}=\frac{6(0.01)^2\times 30\times60}{0.6\times 0.6}$
$\text{h}=3\text{m}$

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