Question

6. Two cylinders have equal volumes. If their radii'are in the ratio 2.1. then find the ratio of their heights​

Answer 1

Let the radii of the two cylinder be 2r and r.

And let the heights be H and h.

Now, their volumes will be $\pi (2r)^2H ~and~ \pi r^2h$

Their ratio are $\frac{\pi (2r)^2H} {\pi r^2h} \\\\\frac{\cancel{\pi(r)^2} 4H} {\cancel{\pi r^2}h} = \frac{4H} {h}$

But the given ratio is 1:1

So, $\frac{4H}{h}= 1 \\\\\sf 4H=h \\\\\sf \frac{H}{h}=\frac{1} {4}$

Hence the ratio is 1:4