Question

Question 24

The ratio of radii of two cylinders is 1 : 2 and heights are in the ratio 2 : 3. The ratio of their volumes is
a) 1 : 6
b) 1 : 9
c) 1 : 3
d) 2 : 9

Answer 1

Let $r_1,r_2$ be radii of two cylinders and $h_1,h_2$ be their heights.
Then, $\frac{r_1}{r_2}=\frac{1}{2}$ and $\frac{h_1}{h_2}=\frac{2}{3}$
Now, $\frac{V_1}{V_2}=\frac{\pi r_1^2{h}_1}{\pi r_2^2{h}_2}={\left(\frac{r_1}{r_2}\right)}^2\times \frac{h_1}{h_2}={\left(\frac{1}{2}\right)}^2\times \frac{2}{3}$
$=\frac{1}{4}\times \frac{2}{3}=\frac{1}{6}=1:6$
Hence, $V_1:V_2=1:6$