A given quantity of metal is to be cast into a solid half circular cylinder with a rectangular base…
Mathematics20256 marksDerivation
A given quantity of metal is to be cast into a solid half circular cylinder with a rectangular base and semi-circular ends. If the total surface is minimum then prove that the ratio of the length of cylinder to the diameter of semi-circular ends is $\pi : \pi + 2$. [Application]
To show: \text{Ratio of length of cylinder to diameter of semi-circular ends} = \pi : \pi + 2
