Question

Question 51

Two cylinders of equal volume have heights in the ratio 1 : 9. The ratio of their radii is ___.

Answer 1

3 : 1
Let $r_1$, $r_2$ be the radii and $h_1$, $h_2$ be the heights of two cylinders.
Given, $\frac{h_1}{h_2}=\frac{1}{9}$
Now, according to the question.,
$\pi r_1^2{h}_1=\pi r_2^2{h}_2$ $[\therefore volumeofcylinder=\pi r^{2}h]$
$\Rightarrow \frac{r_1^2}{r_2^2}=\frac{h_2}{h_1}\Rightarrow {\left(\frac{r_1}{r_2}\right)}^2=\frac{9}{1}\Rightarrow \frac{r_1}{r_2}=\frac{\sqrt{9}}{1}\Rightarrow \frac{r_1}{r_2}=\frac{3}{1}$
Hence, $r_1:r_2=3:1$