Question

9. Water flows at a rate of 10 m per minute through
a cylindrical pipe having its diameter as 20 mm.
How much time will it take to fill a conical vessel
of base diameter 40 cm and depth 24 cm. (HOTS)​

Answer 1

Answer:

3.2 minutes

Step-by-step explanation:

Amount of water required to fill the conical vessel = volume of conical vessel

=1/3π(20)^2 ×24=3200π cu.cm .... (1)

Amount of water that flows out of cylindrical  pipe in 1 minute

=π(1)^2×10×100 =1000π cu.cm....(2)

From (1) & (2)

Time required to fill the vessel=$\frac{3200\pi}{1000\pi}$

=3.2 minutes

​  

Answer 2

Answer:

The time taken to fill a conical vessel is 32 min  .

Step-by-step explanation:

Given as :

The diameter of cylindrical pipe = d = 20 mm

The radius of cylindrical pipe = r = $\dfrac{d}{2}$

r = $\dfrac{20}{2}$  = 10 mm

Again

The diameter of conical vessel = D = 40 cm

The radius of conical vessel = R = $\dfrac{D}{2}$

i.e  R = $\dfrac{40}{2}$ = 20 cm = 200 mm

Height of conical vessel = H = 24 cm = 240 mm

Amount of water required to fill the conical vessel  = volume of conical vessel

∵ volume of conical vessel = $\dfrac{1}{3}$ × π × R² × H

Or,  V  = $\dfrac{1}{3}$ × 3.14 × (200 mm)² × (240 mm)

∴  volume of conical vessel = V = 10048000 cubic mm            

Or,   V = 10048  cubic m         .......1

Again

 Amount of water that flows out of cylindrical pipe per min =  π × r² × h

Or,   Amount of water that flows out of cylindrical pipe per min =  3.14 × 0.01² × 10

∴  Amount of water that flows out of cylindrical pipe per min = 0.00314 cubic m  ......2

From (1) & (2)

Time required to fill the vessel =   $\dfrac{10048}{0.00314}$

Or,  Time = 32 min

So, The time taken to fill a conical vessel = T = 32 min

Hence, The time taken to fill a conical vessel is 32 min  . Answer