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प्रश्न
A vessel in the shape of cuboid ontains some water. If these identical spheres are immersed in the water, the level of water is increased by 2cm. if the area of base of cuboid is 160cm2 and its height 12cm, determine radius of any of spheres?
उत्तर
Given that area of cuboid = 160cm2
Level of water increased in vessel = 2cm
Volume of a vessel = 160 x 2cm3 .......(1)
Volume of each sphere =`4/3pir^3cm^3`
Total volume of 3 spheres `=3xx4/3pir^3cm^3` ...........(2)
Equating (1) and (2) ∵Volumes are equal V1 = V2
`160xx2=3xx4/3pir^3`
`r^3=(160xx2)/(3xx4/3pi)
`r^3=320/(4pi)`
r = 2.94cm
∴ Radius of sphere = 2.94cm
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