# 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 - Mathematics

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)    ∵Volumes 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

Concept: Volume of a Combination of Solids
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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 14 Surface Areas and Volumes
Exercise 14.1 | Q 45 | Page 30