Water from 1000 spherical vessels of radius 10 cm. is poured to a vessel of bigger radius. If bigge

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19 Sep 2011 sphere

Water from 1000 spherical vessels of radius 10 cm. is poured to a vessel of bigger radius. If bigger vessel is completely filled by the water of smaller spheres, then what will be the radius of bigger.

OPtion

1) 10000 cm.
2) 20 cm.
3) 50 cm.
4) 1000 cm.
5) 100 cm.
6) is not possible to solve
7) 60 cm.
8) 80 cm.
9) 120 cm.
10) none of these

Solution

volume depends on 3 powers of radius so new radius = 10 cm. * (1000)^1/3
= 10*10 cm. = 100 cm.

Correct Option: 5 Best Solution (8)

~Sandeep~   13 years AGO

Volume of a sphere = (4/3)*(pi*R^3)
Volume of 1000 smaller sphere = Volume of Bigger sphere
=> 1000*(4/3)*pi*r^3 = 1000*(4/3)*pi*R^3
putting r=10cm and solving we get
=> 1000*10^3 = R^3
R=100cm

Like? Yes (6) | No (2)  

Karan   13 years AGO

Radius of bigger sphere = cube root of (1000*10^3)= 10*10=100 cms

Like? Yes (3) | No (2)  

harikrishnan   13 years AGO

volume of bigger spr = 1000* vol of small spr
4/3*3.14*R3 = 1000*4/3* 3.14 * 10*10*10
R3 = 1000000
R = 100 cm

Like? Yes (2) | No (1)  

SWARNIMA UMARI   13 years AGO

vol of one small sphere= 4/3*22/7*10^3 hence vol of 1000 small sphere= 4/3*22/7*10^3*1000.
this vol will be equal to vol of bigger sphere.
now let radius of big sphere= R
hence 4/3*22/7*10^3*1000= 4/3*22/7*R^3
R^3=10^3*10^3
hence R= 100cm

Like? Yes (2) | No (2)  

Dr.Dipin Singh   13 years AGO

If v is volume of smaller vessel with radius 10 cms
and If V is volume of smaller vessel with radius R cms , then
V=1000*v
(4/3)*pi*R^3 = 1000*(4/3)*10^3
or
R^3= 10^6
R=10^2=100 cms

Like? Yes (3) | No (4)  

virendra   13 years AGO

1000*(4/3 pie(10)^3)
=4/3 pie(10)^6
so radius = 10^2=100

Like? Yes (1) | No (2)  

jai Narayan Mishra   13 years AGO

let radius of smaller vessels are 'r' and that of bigger vessels are 'R'..Now
1000*[(4/3)*3.14*(r^3)]= (4/3)*3.14*(R^3)
As r=10 cm, by putting the value or r in above equation we get R=100 cm..which is the answer

Like? Yes (1) | No (2)  

Soumya Parhi   13 years AGO

Volume of a sphere is (4/3)*3.14*r^3
so 1000 vessels of radius 10 cm can keep water of volume 1000*(4/3)*3.14*10^3...(i)
Let putting this volume of water into a bigger vessle we need radius R.
Now the volume of bigger vessel is (4/3)*3.14*R^3...(ii)
As both will contain same amount of water equating equation (i) &(ii) we get
1000*(4/3)*3.14*10^3=(4/3)*3.14*R^3
=>R^3=1000000
=>R=100
So the radius of bigger vassel is 100cm

Like? Yes (2) | No (4)