Water flows at the rate of 10 m per mins from a cylindrical pipe of radius 2.5

Question

Water flows at the rate of 10 m per mins from a cylindrical pipe of radius 2.5 mm. A conical vessel of diameter 40 cm and depth 24 cm is filled with water flowing from this pipe. The time taken to fill the conical vessel is:

Options:

A . < 30 mins

B . 30 < t < 50 mins

C . 50 < t < 75 mins

D . >75 mins

Answer: Option C
:
C

Area= $π$ r $^{2}$ =6.25 $π$

Rate of flow= (

π

^{2}

x1000) mm

^{3}

/min
=6250

π

^{2}

/min
Volume of cone=

\frac{1}{3}

π

^{2}

h =

\frac{1}{3}

π

(200)

^{2}

x 240 mm

^{3}

=80

π

x40000
=3200000

π

^{3}

Thus, total time taken is:

\frac{(V o l u m e o f c o n e i n m m^{3})}{(R a t e o f w a t e r f l o w i n m m^{3} / m i n)}

= 51.2min
Thus answer option (c) is correct.

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