Question

The radii of two right circular cylinders are in the ratio 2 : 3 and their heights are in the ratio 5:4.
Calculate the ratio of their volumes.​

Answer 1

Answer 5:9

ratio of radii = 2 : 3

so the radius = 2x & 3x

ratio of heights = 5 : 4

heights = 5y & 4y

volume of the cylinder ,

$= \pi {r}^{2} h$

volume of cylinder 1

$= \pi ({2x}^{2} )5y \\ = \pi4 {x}^{2} 5y \\ =\pi 20 {x}^{2} y$

volume of cylinder 2

$= \pi ({3x}^{2} )4y \\ = \pi9 {x}^{2} 4y \\ = \pi36 {x}^{2} y$

ratio between the volumes

20 : 36

= 5 : 9

hope this will help

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Answer 2

Step-by-step explanation:

Let the radius of the first be 2r; then the radius of the second is 3r

Let the height of the first be 5h; then the height of the second is 4h

volume cylinder = π × radius² × height

→ volume first = π × (2r)² × 5h = 20πr²h

→ volume second = π × (3r)² × 4h = 36πr²h

→ ratio of their volumes is:

20πr²h : 36πr²h

= 20 : 36 (divide by πr²h)

= 5 : 9 (divide by 4)