Question

The volume of two cylinders are as a:b and their heights are c:d. Find the ratio of their diameters

Answer 1

hope u will find the solution useful

Answer 2

Answer: The ratio of diameters would be

$\dfrac{r_1}{r_2}=\dfrac{\sqrt{ad}}{\sqrt{bc}}$

Step-by-step explanation:

Since we have given that

Ratio of volume of two cylinders = a:b

Ratio of heights = c:d

As we know the formula for "volume of cylinders":

$\dfrac{\pi r_1^2h_1}{\pi r_2^2h_2}=\dfrac{a}{b}\\\\\dfrac{r_1^2c}{r_2^2d}=\dfrac{ab}{bc}\\\\\dfrac{r_1^2}{r_2^2}=\dfrac{ad}{bc}\\\\\dfrac{r_1}{r_2}=\dfrac{\sqrt{ad}}{\sqrt{bc}}$

As we know that ratio of radius is equal to ratio of diameter.

so, the ratio of diameters would be

$\dfrac{r_1}{r_2}=\dfrac{\sqrt{ad}}{\sqrt{bc}}$