Question

the base raddii of two circular cones of same height are in the ratio 3 is to 5.find ratio of their volumes​

Answer 1

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Given :-

$\sf{For \: two \: circular \: cones-}$

$\sf{base \: radius \: is \: same.}$

$\sf{r1 = r2 = r}$

$\sf{Ratio \: of \: their \: heights-}$

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

To Find :-

$\sf{Ratio \: of \: volumes \: of \: these \: 2 \: circular \: cones-}$

$\sf{\dfrac{V1}{V2} = ?}$

Using Formulas :-

$\sf{Volume \: of \: Circular \: Cone =\dfrac{1}{3} \pi r^{2} h}$

Solution :-

$\sf{For \: first \: Circular \: cone-}$

$\sf{height = h1 = 3}$

$\sf{Volume = V1 =\dfrac{1}{3} \pi r^{2} h1}$

$\sf{For \: second \: Circular \: cone-}$

$\sf{height = h2 = 5}$

$\sf{Volume = V2 =\dfrac{1}{3} \pi r^{2} h2}$

$\sf{Now \: ,}$

$\sf{V1 =\dfrac{1}{3} \pi r^{2}\times 3}$

$\sf{V1 = \pi r^{2}}$ ---(1)

$\sf{V2 =\dfrac{1}{3} \pi r^{2}\times 5}$

$\sf{V2 =\dfrac{5}{3} \pi r^{2}}$

$\sf{From \: equation \: (1)-}$

$\sf{V2 =\dfrac{5}{3}\times V1}$

$\sf{\dfrac{V2}{V1}=\dfrac{5}{3}}$

$\sf{\dfrac{V1}{V2}=\dfrac{3}{5}}$

Result :-

$\sf{Ratio \: of \: the \: volumes \: of \: these \: 2 \: Circular}$

$\sf{cones \: is \: same \: as \: the \: ratio \: of \: their}$

$\sf{heights.}$

Extra Formulas :-

1)$\sf{Total \: Surface \: Area =\pi r(r + h)}$

2)$\sf{Curved \: Surface \: Area =\pi r l}$

3)$\sf{Slant \: height(l) =\sqrt{r^{2} + h^{2}}}$

Answer 2

3: 5

hope it helps you....