19 SEP 2011 sphere Water from 1000 spherical vessels of radius 10 cm. is poured to a vessel of bigg

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12 Jul 2021 Radius

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) 70 cm.
7) 60 cm.
8) 80 cm.
9) 120 cm.
10) none of these

Solution

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

Correct Option: 5 Best Solution (4)

G.S.Kantharao   3 years AGO

4/3(πR^3)=1000*4/3(πr^3)
R^3=1000*10^3=>R=100cm
My option is 5👈

Like? Yes (2) | No   

Billal Hossain   3 years AGO

Small Sphere's volume = 4/3*π*r^3
= 4/3*π*10^3
=4/3*π*1000
Then, 1000 vessels volume = 1000*4/3*π*1000
=4/3*π*1000000
A bigger vessel volume= 4/3*π*R^3
According to question,
4/3*π*R^3= 4/3*π*1000000
Or, R^3=1000000
Or, R= 100
Therefore, Bigger Radius = 100 cm
Hence, My option is (5)

Like? Yes (1) | No   

SAYAN CHATTERJEE   3 years AGO

4/3πr^3*1000= 4/3πR^3
R= 100.
Option 5.

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Chinmay Swarup Chiranjeevi   3 years AGO

Area of big sphere = 1000 x Area of small sphere
pi x R^3 = 1000 x pi x r^3
pi x R^3 = 1000 x pi x 10 x 10 x 10
R = 100

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