Question

The ratio of the base radius of two right cylinder in 1:2.If ratio of their volume is 5:12.Find the ratio of their Height.​

Answer 1

$\huge{\mathbb{\red{ANSWER:-}}}$

For two right Circular Cylinder :-

Given :-

The radius of the first cylinder is r1 and the radius of the Second cylinder is r2 .

Volume of the first cylinder is V1 and volume of the second cylinder is V2 .

The height of the first cylinder is h1 and the height of the second cylinder is h2 .

$\sf{\dfrac{r1}{r2} =\dfrac{1}{2}}$

$\sf{\dfrac{V1}{V2} =\dfrac{5}{12}}$

To Find :-

$\sf{Ratio \: of \: the \: heights \: of \: two \: circular \: cylinder -}$

$\sf{\dfrac{h1}{h2} = ?}$

Using Formula :-

$\sf{Volume \: of \: right \: Circular \: Cylinder =\pi r^{2} h}$

Solution :-

$\sf{For \: first \: right \: Circular \: Cylinder-}$

$\sf{Volume (V1) =\pi (r1)^{2}h1}$

$\sf{For \: Second \: right \: Circular \: Cylinder-}$

$\sf{Volume (V2) =\pi (r2)^{2} h2}$

$\sf{\dfrac{V1}{V2} =\dfrac{(r1)^{2} h1}{(r2)^{2} h2}}$

$\sf{\dfrac{5}{12} =(\dfrac{r1}{r2})^{2} (\dfrac{h1}{h2})}$

$\sf{\dfrac{5}{12} =(\dfrac{1}{4})(\dfrac{h1}{h2})}$

$\sf{\dfrac{h1}{h2} =(\dfrac{5}{12})(\dfrac{4}{1})}$

$\sf{\dfrac{h1}{h2} =\dfrac{5}{3}}$

As We got :-

h1 : h2 = 5 : 3

Extra Related Formulas for right Circular Cylinder :-

1)$\sf{TSA = 2\pi r(r + h)}$

2)$\sf{CSA = 2\pi r h}$

3)$\sf{Volume = base \: area\times height}$