Two circular cylinders of equal volumes have their heights in the rati

1.	Two circular cylinders of equal volumes have their heights in the ratio 1 : 2. Find the ratio of their radius.
Answer» Given, Volume of cylinder 1 = volume of cylinder 2 Ratio of their height = 1 : 2 = \(\frac{h_1}{h_2}\) = \(\frac{1}{2}\) We have, = V₁ = V₂ = πr¹₂h₁ = πr²₂h₂ = \(\frac{r^2_1}{r^2_2}\) = \(\frac{2}{1}\) = \(\frac{r_1}{r_2}\) = \(\sqrt{\frac{2}{1}}\) = \({\frac{\sqrt2}{1}}\) Volume of the cylinder is given by: \(V = \pi r^2h\) Where r is the radius and h is the height of the cylinder. We know that: \(V_1 = V_2 \space\text{and}\space h_1 = 2h_2\) Therefore: \(\pi r_1^22h_2 = \pi r_2^2h_2\implies \frac{r_2}{r_1}=\sqrt2\)

Two circular cylinders of equal volumes have their heights in the ratio 1 : 2. Find the ratio of their radius.

Answer»

Given,

Volume of cylinder 1 = volume of cylinder 2

Ratio of their height = 1 : 2

= \(\frac{h_1}{h_2}\) = \(\frac{1}{2}\)

We have,

= V₁ = V₂

= πr¹₂h₁ = πr²₂h₂

= \(\frac{r^2_1}{r^2_2}\) = \(\frac{2}{1}\)

= \(\frac{r_1}{r_2}\) = \(\sqrt{\frac{2}{1}}\) = \({\frac{\sqrt2}{1}}\)

Volume of the cylinder is given by:

\(V = \pi r^2h\)

Where r is the radius and h is the height of the cylinder.

We know that:

\(V_1 = V_2 \space\text{and}\space h_1 = 2h_2\)

Therefore:

\(\pi r_1^22h_2 = \pi r_2^2h_2\implies \frac{r_2}{r_1}=\sqrt2\)