Out of three jars of equal diameter and height, `2/3` part of the first, `5/6` part of the second and `7/9` part of the third were filled with dilute sulphuric acid. Whole of acid in the three jars were poured into a large jar of `2*1` dcm diameter, as a result the height of acid in the jar becomes `4*1` dcm. If the length of diameter of each of the three equal jars is `1*4` dcm. Calculate the height of three jars.

Explanation

Let the height of three jars be h dcm.
So the volume of the acid in the large jar
`=(22)/(7)xx (2.1/2)^(2) xx 4.1` cubic.dcm `= (22)/(7) xx 1.05xx1.05xx4.1` cubic-dcm `= 14.2065` cubic-dcm
As per question,
`2/3 xx (22)/(7)xx(1.4/2)^(2) xx h + 5/6xx22/7xx(1.4/2)^(2)h+7/9xx22/7xx(1.4/2)^(2)xxh=14.2065`.
or, `22/7xx(0.7)^(2)xxh (2/3+5/6+7/9)=14.2065` or, `22xx0.1xx0.7xxhxx(12+15+14)/(18)=14.2065`
or, `1.54hxx(41)/(18)= 14.2065` or, `h=(14.2065xx18)/(1.54xx41)=4.05`
Hence the required height of the jar `= 4.05` dcm.