Question

The radius of the base of a cylinder and a cone are in the ratio 3:5. What is the ratio of their volumes

Answer 1

$\huge{\red{\underline{\underline{Answer:-}}}}$

Proper Question:

The radii of the base of a cylinder and cone is in the ratio 3:4 and the heights are in the ratio 2:3. The ratio between the volume of the cylinder to that of cone is?

Given:

Ratio of radius of base of cylinder and cone is 3:4

Ratio of height of cylinder and cone is 2:3

To find:

Volume of cylinder to that of cone = ?

Solution:

Let R and R' be the radii of base of cylinder and cone. H and H' be the height of cylinder and cone

R/R' = 3/4

H/H' = 2/3

Volume of cylinder = πR²H

Volume of cone = πR'²H'

Volume of cylinder/ Volume of cone =

πR²H/ 1/3 π R'²H'

= 3 × (3/4)² × (2/3)

= 3 × 9/16 × 2/3

= 9/8

Required answer:

Therefore, the ratio of volume of cylinder to volume of cone is 9:8