Question

if the ratio of the volumes of two cones 2:3 and the ratio of their bases is 1:2 find the ratio of their heights​

Answer 1

$\huge{\textbf{\underline{Required Ratio:-}}}$

$\large {\textbf{ \dfrac{h_1}{h_2}= \dfrac{8}{3} }}$

$\huge{\textbf{\underline{Correct Question:-}}}$

Q.If the ratio of the volumes of two cones 2:3 and the ratio of the radii of their bases is 1:2 find the ratio of their heights.

$\huge{\textbf{\underline{Solution:-}}}$

Let the radii of their bases is $r_1$ and $r_2$.

$\dfrac{V_1}{V_2}= \dfrac{\dfrac{1}{3}\pi r^2_1h_1}{\dfrac{1}{3}\pi r^2_2 h_2}$

• Cancel 1/3 and π.

$\dfrac{V_1}{V_2}= \dfrac{r_1^2h_1}{r_2^2 h_2}$

$\dfrac{2}{3}= \dfrac{(1)^2 h_1}{(2)^2h_2}$

$\dfrac{2}{3}= \dfrac{h_1}{4h_2}$

$8h_2= 3h_1$

$\therefore \textbf{ \dfrac{h_1}{h_2}= \dfrac{8}{3} }$