The ratio of the radii of two cylinders is 1: √3 and their heights a

1.	The ratio of the radii of two cylinders is 1: √3 and their heights are in the ratio 2 : 3. The ratio of their volumes is(a) 1 : 9 (b) 2 : 9 (c) 4 : 9 (d) 5 : 9
Answer» (b) 2 : 9 Required ratio = \(\frac{πr^2_1h_1}{πr^2_1h_2}\) = \(\bigg(\frac{r_1}{r_2}\bigg)^2\times\frac{h_1}{h_2}\) = \(\bigg(\frac{1}{\sqrt3}\bigg)^2\times\frac23=\frac29\) = 2 : 9.

The ratio of the radii of two cylinders is 1: √3 and their heights are in the ratio 2 : 3. The ratio of their volumes is(a) 1 : 9 (b) 2 : 9 (c) 4 : 9 (d) 5 : 9

Answer»

(b) 2 : 9

Required ratio = \(\frac{πr^2_1h_1}{πr^2_1h_2}\) = \(\bigg(\frac{r_1}{r_2}\bigg)^2\times\frac{h_1}{h_2}\)

= \(\bigg(\frac{1}{\sqrt3}\bigg)^2\times\frac23=\frac29\) = 2 : 9.