M4maths Previous Puzzles

19 Aug 2016 Conical Vessel

Water flows at the rate of 10 m per min. from a cylindrical pipe 5 mm in diameter. How long will it take to fill up a conical vessel whose diameter at the base is 40 cm and depth 24 cm?

OPtion

1) 48 min. 15 sec.
2) 51 min. 12 sec.
3) 46 min. 35 sec.
4) 61 min. 15 sec.
5) 54 min. 22 sec.
6) 58 min. 15 sec.
7) 54 min. 6 sec.
8) 52 min. 1 sec.
9) 55 min. 15 sec.
10)None of these

Solution

Volume flown = 1/3 PI (20)^2 * 24 = 3200 Pi
Volume flown in 1 min = (Pi* 2.5/10 * 2.5/10 * 1000) = 62.5 Pi
Therefore Time taken = 3200 Pi / 62.5 Pi = 51 min. 12 sec.

Option 2)

Correct Option: 2 Best Solution (22)

aishwarya pandey   8 years AGO

Radius of the pipe = 5/2 mm = 5/2 x 1/10 cm = 1/4 cm

Speed of water = 10 m/min = 1000 cm/min

Volume of water that flows in 1 minute = Π r2 h = 22/7 x 1/4 x 1/4 x 1000 = 1375/7 cm3

Radius of conical vessel = 40/2 = 20 cm; Depth = 24 cm

Therefore, Capacity of the vessel = 1/3 x Π r2 h

= 1/3 x 22/7 x 20 x 20 x 24 = 70400/7 cm3

Therefore, Time required to fill the vessel = capacity of the vessel / volume of water flowing per minute

= 70400/7 / 1375/7 = 70400/7 x 7/1375 = 256/5 minutes = 51 min 12 sec

Like? Yes (171) | No (47)  

Sandip Das   8 years AGO

cylindrical pipe diameter is 5mm=5/10 cm
radius is =5/20=1/4 cm
speed of the water 10 m/min=1000cm/min
volume of water that flow in 1 min= (22/7)*(1/4)^2*1000
=1375/7 cm^3
radius of conical vesel 40/2=20 cm
depth 24 cm
volume =(1/3)*(22/7)*(20)^2*(24)
=70400/7 cm^3
time required to fill the vessel is=(70400/7)/(1375/7)
=256/5 min
=51 min 12 sec (option 2)

Like? Yes (37) | No (25)  

DEVANSH SUBNANI   8 years AGO

Let radius of cylindrical pipe be r
Suppose radius and height of conical vessel be R and H respectively.Therefore,
r=(1/4)cm ,2R=40
R=20cm,H=24cm
Volume of conical vessel=(1/3)*(22/7)*(20)sq*24
Rate of water flow=10m/min=1000cm/min
Therefore,Volume of water flowing out of the pipe in 1min=(22/7)*(1/4)sq*1000
Let time taken to fill conical vessel be t minutes
Therefore,Volume of water flowing out of pipe in t minutes=(22/7)*(1/4)sq*1000t
Volume of water flowing out of pipe in t minutes=volume of conical vessel
Therefore,(22/7)*(1/16)*1000t=(1/3)*(22/7)*400*24
Therefore,t=51.2
Thus,time taken to fill the conical vessel is 51.2 minutes
Option 2)

Like? Yes (25) | No (14)  

sruthi pujari   8 years AGO

1.Cone volume=1/3(Ï€*20*20*24)
2.Area of cylinder*velocity*time=volume of cone
=> time=(1/3(Ï€*20*20*24))/(1/2(Ï€*0.025*0.025)*100)=51.2=51 mins12secs

Like? Yes (22) | No (12)  

ABHINAV PUSHPAM   8 years AGO

Radius of the pipe = 5/2 mm = 5/2 x 1/10 cm = 1/4 cm


Speed of water = 10 m/min = 1000 cm/min


Volume of water that flows in 1 minute = ? r2 h = 22/7 x 1/4 x 1/4 x 1000 = 1375/7 cm3


Radius of conical vessel = 40/2 = 20 cm; Depth = 24 cm


Therefore, Capacity of the vessel = 1/3 x ? r2 h


= 1/3 x 22/7 x 20 x 20 x 24 = 70400/7 cm3


Therefore, Time required to fill the vessel = capacity of the vessel / volume of water flowing per minute


= 70400/7 / 1375/7 = 70400/7 x 7/1375 = 256/5 minutes = 51 min 12 sec

Like? Yes (20) | No (13)  

sandeep kumar   8 years AGO

Radius of the pipe = 5/2 mm = 5/2 x 1/10 cm = 1/4 cm
Speed of water = 10 m/min = 1000 cm/min
Volume of water that flows in 1 minute = Π r2h = 22/7 x 1/4 x 1/4 x 1000 = 1375/7 cm3
Radius of conical vessel = 40/2 = 20 cm; Depth = 24 cm
Therefore, Capacity of the vessel = 1/3 x Π r2h
= 1/3 x 22/7 x 20 x 20 x 24 = 70400/7 cm3
Therefore, Time required to fill the vessel = capacity of the vessel / volume of water flowing per minute
= 70400/7 / 1375/7 = 70400/7 x 7/1375 = 256/5 minutes = 51 min 12 sec

Like? Yes (15) | No (10)  

akanksha singh   8 years AGO

VOL OF CONICAL VESSEL=1/3*3.14*20*20*24
VOL OF PIPE=3.14*(1/4)*(1/4)*1000
TIME TAKEN=VOL OF CONICAL VESSEL/VOL OF PIPE
=51 MIN 12 SEC

Like? Yes (11) | No (7)  

rushi   8 years AGO

Rc=0.5*diameter of conical vessel
Rt=0.5*diameter of tap
rate flow =10m/min=1000cm/min
time taken=((1/3)*pi*Rc*Rc*depth)/(rate of flow*pi*Rt*Rt)
=((1/3)*pi*20*20*24)/(1000*pi*0.25*0.25)
=52.2min
=52min 12sec
=

Like? Yes (28) | No (24)  

Naga   8 years AGO

Volume of water flow in 1 min = volume of cylinder 5mm diameter, 10m height = PI*.25*.25*1000 = 196.4286
volume of cone = PI*20*20*24/3 = 10057.14
time required to fill cone = 10057.14/196.4286
=51.2 minutes

Like? Yes (16) | No (12)  

Mukund Manohar   8 years AGO

radius of pipe = 5/2 * 10 = 5/20 cm
height of pipe = 1000 cm
radius of vessel = 20 cm and height = 24 cm
Volume of water flow in one minute from cylindrical pipe
= pi * (5/20)^2 * 1000 = 125/2 pi cm^3
and volume of conical vessel = 1/3 * pi *20^2 * 24
= 3200pi cm^3
So,Required Time = (3200pi*2)/125pi
= 51 min 12 sec

Like? Yes (11) | No (9)  

Rahul Das   8 years AGO

volume of a conical vessel =(1/3)*pi*r^2*h
= (1/3)*pi*(400/2)^2*240
=10053096.5 mm sqr
volume of a cylindrical pipe =pi*(5/2)^2*10^4
=196349.541 mm sqr
time taken=10053096.5/196349.541 =51.2 min
= 51 min and 12 sec

Like? Yes (14) | No (12)  

yerra anitha   8 years AGO

radious the pipe is 1/4cm
speed of the water is 10m/min
volume of the water that follows in 1minute is 22/7*1/4*1/4*1000 is 1375/7 cm3
soo (70400/7)/(375/7) is 51 min 12 sec

Like? Yes (19) | No (17)  

G.S.Kantharao   8 years AGO

Time taken to fill conical vessel = (Volume of the vessel)/(Volume of water travells per minute)= (Ï€.R^2 H)/3*(Ï€r^2 h)
=R^2 H/3r^2 h= (20^2 .24)/3(1/4 )(1/4)(1000)
(400*24)/(3000)(1/16)=(9600*16)/3000= 9600*16/3000
=(96*16)/30= 256/5= 51minutes and 12 Seconds.
Hence the right choice is 2.

Like? Yes (14) | No (16)  

Rucha   8 years AGO

vo of water =22/7×1/4×1/4×1000=1357/7
capacity=1/3×22/7×20×20=70400/7
70400/7×7/1375=51 min12 sec

Like? Yes (9) | No (11)  

Aditi Paul   8 years AGO

equating volume of water flowing through the pipe and entering the conical flask, let x be time taken..
22/7*(5/2*10^-3)^2*10x=1/3*22/7*(100/2*10^-2)^2*24*10^-2
on solving, we get x=51.2 min= 51 min 12 seconds

Like? Yes (8) | No (10)  

RISHABH   8 years AGO

Volume flown in conical vessel = 1/3*22/7*(20)^2*24
=22/7*3200
Volume flown in 1 minute = 22/7*(2.5/10)^2*1000
=22/7*62.5
So, time taken = (3200*22/7)/(62.5*22/7)
=51 min 12sec

Like? Yes (7) | No (10)  

Manish   8 years AGO

volume is equal then
1/3*22/7*r*r*h=22/7*r*r*h
t=51.12minute

Like? Yes (6) | No (9)  

DHANANJAY KUMAR   8 years AGO

volume of conical vessal is =1/3(pi*20*20*24) cm3
volume filed by the pipe in 1 min =(pi*2.5*2.5*1000) cm3
time =Volume of conical vessel/ volume of the pipe filled in 1 min
ans 51 min 12 sec

Like? Yes (7) | No (10)  

Priyaj   8 years AGO

vol of cone= 1/2 pi R^2 H
vol of water flowing= pi*r^2*1000cm
=pi*(1/4)^2*1000
in x minutes=pi*(1/4)^2*1000*x
x=(400*24*16)/3*1000
=51.2 minutes= 51minutes 12 seconds.

Like? Yes (6) | No (10)  

Aniket Roy   8 years AGO

volume of water flowing from pipe=pi*(1/4)^2*1000
vol. of cone=pi*(20)^2*24=10057.14286
so,time taken to fill the cone=vol. of cone/vol. of water
=10057.14286/196.4285714=51.20000002
so,51min12sec.

Like? Yes (10) | No (14)  

codemaker   8 years AGO

first calculate volume of cylinder covered in 1min with h=10m and r=2.5cm. formula pi*r*r*h.
then calculate volume of cone h=24cm and r=20cm with formula (pi*r*r*h)/3
answer=volume of cone/volume of cylinder in minute

Like? Yes (7) | No (11)  

Surit Datta   8 years AGO

51 min and 12 sec is the answer.
That's it.
Thanks.

Like? Yes (6) | No (18)