Two right circular cylinders of equal volume have their heights in the ratio 1:2. Find the ratio of their radii.

Given: 

Two right circular cylinders with equal volumes.

The heights of the cylinders are in the ratio $1:2$. 

Formula Used: 

Volume of the cylinder = $$\pi r^2 h$$ 

where, r = radius, h = height  

Solution: 

Let the radius of two cylinders are $$r_1 \, and \ \ r_2$$ 

Let the height be $$h_1 \, and \, h_2$$  

​$$\frac{h_1}{h_2} = \frac{1}{2} \implies {h_2} = 2h_1$$ 

Now, 

$$\pi \times {r_1}^2 \times h_1 = \pi \times{ r_2}^2 \times h_2 \\\pi \times{r_1}^2 \times h_1 = \pi \times {r_2}^2 \times 2h_1 \\\implies \frac{{r_1}^2}{ {r_2}^2} = \frac{2}{1} \\ \ \\ \implies \frac{{r_1}}{ {r_2}} = \frac{\sqrt2}{1}$$​​