A test tube consists of a hemisphere and a cylinder of the same radius. The volume of the water required to fill the whole tube is `5159/6 cm^3` and `4235/6 cm^3` of water required to fill the tube to a level which is 4 cm below the top of the tube. Find the radius of the tube and the length of its cylindrical part.

Explanation

Volume of test tube=`2/3pir^3+pir^2h=5159/6-(1)`

Fill upto (h-4)=`2/3pir^3+pir^2(h-4)=4235/6-(2)`

subtracting equation 2 from equation 1

`pir^2=924/24=38.5`

`r^2=(3.5)^2`

`r=3.5cm`

`V=2/3pir^3+pir^2h=5159/6`

`2/3*22/7*(3.5)^2+pi(3.5)^2h=5159/6`

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