Question

the heights of two cylinders are in the ratio of 5:3 and their volume are in the ratio 20:27. then the ratio of their radius is...... ?

plz its urgent

Answer 1

Answer:

The ratio of their radius is $2:3$

Step-by-step explanation:

Volume of cylinder is $\pi r^2h$, where r is radius and h is height

We have

The heights of two cylinders are in the ratio of $5:3$

$\frac{h_1}{h_2} =\frac{5}{3}$

The volume are in the ratio $20:27$

$\frac{V_1}{V_2} =\frac{20}{27}\\\\\frac{\pi r_1^2h_1}{\pi r_2^2h_2} =\frac{20}{27}\\\\\frac{ r_1^2}{ r_2^2}\times \frac{3}{5} =\frac{20}{27}\\\\\frac{ r_1^2}{ r_2^2} =\frac{4}{9}\\\\\frac{ r_1}{ r_2} =\frac{2}{3}$

The ratio of their radius is $2:3$

Answer 2

Answer:

2 : 3

Step-by-step explanation:

Let,

Radius of cylinder 1 = R

Radius of cylinder 2 = r

Now,

We know that

Volume of cylinder = πr²h

=> πR²h/πr²h' = 20/27

=> R² × 5/r² × 3 = 20/27

=> R²/r² = 20/27 × 3/5

=> R²/r² = 4/9

=> R/r = √(4/9)

=> R/r = 2/3

=> R : r = 2 : 3