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Water flows at the rate of 10m/minute through a cylindrical pipe 5 mm in diameter. How long would it take to fill a conical vessel whose diameter at the base is 40 cm and depth 24 cm?

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An Intiative by Sri Chaitanya

51 min, 20 sec

60 min

58 min, 10 sec

54 min, 30 sec

answer is A.

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Detailed Solution

It is given that water flows at the rate of h=10 m/min=1000cm/min
Diameter of cylindrical pipe d=5 mm= 0.50cm.
Diameter of conical vessel = 40cm
Depth of conical vessel=
Obtaining the volume of a conical vessel by using the formula

V = 13 π r 2 h

.
The radius of a conical vessel is,

r = d 2 r = 402 r = 20 cm

The volume of the conical vessel is,

V = 13 π 20224 = 13 π × 400 × 24 = 3.14 × 400 × 8 V = 10053 cm 3

Obtaining the amount of water that flows out of the cylindrical pipe in 1 minute. The radius of a cylindrical pipe is,

r = d 2 r = 52 r = 2.5 mm r = 0.25 cm

The volume of the cylindrical pipe,

V t = π r 2 h V t = π 0.25 2 × 10 m / min V t = π 0.25 2 × 1000 cm / min V t = 196.34 cm 3

The time needed to fill up the conical vessel.

t = 10053 196.34 t = 51.20 min

The conical tank will fill in 51 min. and 20 sec.
Hence, option 1 is correct.

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