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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

Solution:

Given, water flows at the rate of 10m/min through a cylindrical pipe of 5 mm in diameter.

A conical vessel has a diameter at base 40 cm and depth 24 cm.

We have to find the time required to fill the conical vessel.

Volume of cylinder = πr²h

Given, diameter = 5 mm

Radius = 5/2 = 2.5 mm

1 cm = 10 mm

So, r = 2.5/10 = 0.25 cm

Rate of flow = 10m/min

1 m = 100 cm

So, rate of flow = 10(100) cm/min

Volume of water that flows out in 1 minute = π(0.25)²(10)(100)

= 62.5π cm³

Volume of conical vessel = (1/3)πr²h

Given, diameter = 40 cm

Radius = 40/2 = 20 cm

Depth h = 24 cm

= (1/3)π(20)²(24)

= 400π(8)

= 3200π cm³

Given, time required to fill the vessel = volume of conical vessel/volume of water that flows out of cylindrical pipe in one minute

= 3200π/62.5π

= 3200/62.5

= 51.2 minutes.

Therefore, the time required to fill the conical vessel is 51.2 minutes.

✦ Try This: Water flows at the rate of 10m/minute through a cylindrical pipe 4 mm in diameter. How long would it take to fill a conical vessel whose diameter at the base is 30 cm and depth 14 cm?

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 13

NCERT Exemplar Class 10 Maths Exercise 12.4 Problem 5

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

Summary:

Water flows at the rate of 10m/minute through a cylindrical pipe 5 mm in diameter. It takes 51.2 minutes to fill a conical vessel whose diameter at the base is 40 cm and depth 24 cm

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