Question

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?

Answer 1

Let the time taken by pipe to fill vessel = t minutes

Since water flows 10 m in 1 minute, it will flow 10t meters in t minutes.

According to the question,

Volume of conical vessel = Volume of water that passes through pipe in t minutes

Consider conical pope

Base diameter = 40 cm

Base radius, r = 20 cm

Height, h = 24 cm

We know that the volume of cone = `1/3 π"r"^2"h"`

Volume of conical vessel = `1/3π(20)^2(24)` = 3200π cm³

Consider cylindrical pipe

Base diameter = 5 mm = 0.5 cm

Base radius, r = 0.25 cm

Water covers 10t m distance in pipe,

Hence, we get,

Height, h = 10t m = 1000t cm

We also know that,

Volume of a cylinder = πr²h

Volume of water passed in pipe = π(0.25)²(1000t) = 62.5tπ cm³

So, we have

62.5tπ = 3200

62.5t = 3200

t = 51.2 minutes

We know that,

0.2 minutes = 0.2(60) seconds = 12 seconds

Therefore, t = 51 minutes 12 seconds