Half of a tank of length 21 dcm , breadth 11 dcm and depth 6 dcm and depth 6 dcm is full of water . If 100 spheres made of iron and of diameter 21 cm each are fully immeresed into this water of tank , then how many dcm of the water - level of the tank will be raised ?

Explanation

The length of the tank = 21 dcm
breadth of the tank = 11 dcm , and
depth of the tank = 6 dcm
Let the water - level of the tank rises x dcm after the complete immersion of 100 oiron - spheres
` :. ` the volume of the raised - water = `(21 xx 11 xx x)` cubic - dcm
Again , diameter of each sphere = 21 cm
` :. ` radius of each sphere = `21/2 ` cm = `(21)/(2 xx 10) ` dcm = 1.05 dcm
` :.` the volume of 100 iro - spheres ` = 100 xx 4/3 xx 22/7xx (105)^(3) ` cubic - dcm
As per question , ` 21 x 11 xx x = 100 xx 4/3 xx 22/ 7 xx (1.05)^(3)`
` rArr x = ( 100 xx 4 xx 22 xx 1.05 xx 1.05 xx 1.05 )/(3 xx 7 xx 21 xx 1)`
` = ( 100 xx 4 xx 22 xx 105 xx 105 xx 105 )/(3 xx 7 xx 21 xx 11 xx 100 xx 100 xx100 )`
= 2.1
Hence the water - level of the tank will rise 2.1 dcm