Question

Cylinder A and Cylinder B are mathematically similar. The length of cylinder A is 4 cm. The length of cylinder B is 6cm. The volume of Cylinder A is 80cm cubed. Calculate the volume of cylinder B

Answer 1

volume of B is 270 cm³

Explanation:

given 2 similar cylinders with ratio of lengths = a : b , then

ratio of volumes = a³ : b³

here the ratio of lengths = A : B = 4 : 6 = 2 : 3 , then

ratio of volumes = 2³ : 3³ = 8 : 27

let V be the volume of cylinder B , then by proportion

`(volumeA)/(volumeB)` =
`(8)/(27)` , that is

`(80)/(V)` =
`(8)/(27)` ( cross- multiply )

8V = 80 × 27 = 2160 ( divide both sides by 8 )

V = 270

That is the volume of cylinder B = 270 cm³