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Surface Area And Volume of A Right Circular Cylinder — Maths STD 9 — Question

Maharashtra BoardEnglish MediumSTD 9MathsSurface Area And Volume of A Right Circular Cylinder4 Marks
Question
Water flows out through a circular pipe whose internal diameter is 2cm, at the rate of 6 meters per second into a cylindrical tank. The water is collected in a cylindrical vessel radius of whose base is 60cm. Find the rise in the level of water in 30 minutes?
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Answer

Given data is as follows: Internal diameter of the pipe = 2cm Water flow rate through the pipe = 6m/ sec Radius of the tank = 60cm Time = 30 minutes The volume of water that flows for 1 sec through the pipe at the rate of 6m/ sec is nothing but the volume of the cylinder with n = 6 Also, given is the diameter which is 2cm. Therefore, R = 1cm Since the speed with which water flows through the pipe is in meters/ second, let us convert the radius of the pipe from centimeters to meters. Therefore,$\text{r}=\frac{1}{100}\text{m}$
Volume of water that flows for 1 sec $=\frac{22}{7}\times\frac{1}{100}\times\frac{1}{100}\times6$ Now, we have to find the volume of water that flows for 30 minutes. Since, speed of water is in metres/second, let us convert 30 minutes into seconds. It will be 30 × 60 Volume of water that flows for 30 minutes$=\frac{22}{7}\times\frac{1}{100}\times\frac{1}{100}\times6\times30\times60$
Now, considering the tank, we have been given the radius of tank in centimeters. Let us first convert it into metres. Let radius of tank be ‘R’. R = 60cm$\text{R}=\frac{60}{100}\text{m}$
Volume of water collected in the tank after 30 minutes = Volume of water that flows through the pipe for 30 minutes$=\frac{22}{7}\times\frac{60}{100}\times\frac{60}{100}\times6$
$=\frac{22}{7}\times\frac{1}{100}\times\frac{1}{100}\times6\times30\times60$
$\text{h}=3\text{m}$
Therefore, the height of the tank is 3 metres.

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