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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 - CBSE Class 10 - Mathematics

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Question

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?

Solution

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)    āˆµVolumes are equal V= V2

`160xx2=3xx4/3pir^3`

`r^3=(160xx2)/(3xx4/3pi)

`r^3=320/(4pi)`

r = 2.94cm

∴ Radius of sphere = 2.94cm

  Is there an error in this question or solution?

APPEARS IN

 RD Sharma Solution for 10 Mathematics (2018 to Current)
Chapter 14: Surface Areas and Volumes
Ex. 14.10 | Q: 45 | Page no. 30
Solution 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 Concept: Volume of a Combination of Solids.
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