A water tank has the shape of an inverted circular cone with its axis vertical and vertex lowermost. Its semi-vertical angle is . Water is poured into it at a constant rate of 5 cubic meter per hour. The rate at which the level of the water is rising at t

Question

A water tank has the shape of an inverted circular cone with its axis vertical and vertex lowermost. Its semi-vertical angle is $\tan^{- 1} (0.5)$ . Water is poured into it at a constant rate of 5 cubic meter per hour. The rate at which the level of the water is rising at the instant when the depth of water in tank is 4 m is (Take $π = \frac{22}{7}$ )

Smart Achievers · Accepted Answer

(4)

$r = \frac{h}{2}$

$\Rightarrow V = \frac{1}{3} π r^{2} h = \frac{π h^{3}}{12}$

$\frac{d V}{d t} = \frac{π}{4} h^{2} \frac{d h}{d t}$ $= 5$ $\Rightarrow \frac{d t}{d t}]_{h = 4} = \frac{20}{π} \times \frac{1}{16} = \frac{35}{88} m/h$

Solution

1 $1 m/h$

2 $\frac{30}{17} m/h$

3 $\frac{70}{88} m/h$

4 $\frac{35}{88} m/h$

Ans.
(4)

$r = \frac{h}{2}$

$\Rightarrow V = \frac{1}{3} π r^{2} h = \frac{π h^{3}}{12}$

$\frac{d V}{d t} = \frac{π}{4} h^{2} \frac{d h}{d t}$ $= 5$ $\Rightarrow \frac{d t}{d t}]_{h = 4} = \frac{20}{π} \times \frac{1}{16} = \frac{35}{88} m/h$

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Solution

1 1 m/h

2 3017 m/h

3 7088 m/h

4 3588 m/h