Question

Cylinders A and B are similar. The volume of cylinder A is 20mm3. Calculate the volume of cylinder B.

Answer 1

The question is incomplete. The complete question is :

Cylinders A and B are similar. The length of the cylinder A is 4 mm and the length of cylinder B is 6 mm. The volume of cylinder A is 20mm3. Calculate the volume of cylinder B.

Answer:

67.5
`mm^3`

Explanation:

Given that :

Cylinder A and cylinder B are similar.

Let volume of cylinder A = 20
`mm^3`

We know the volume of a cylinder is given by V =
`$\pi r^2 h$`

where, r is the radius of the cylinder

h is the height of the cylinder

We have to find the scale factor.

The length scale factor is =
`$(6)/(4)$`

`$=(3)/(2)$`

Area scale factor
`$=\left((3)/(2)\right)^2$`

`$=(9)/(4)$`

∴ Volume scale factor
`$=\left((3)/(2)\right)^3$`

`$=(27)/(8)$`

Therefore, the volume of cylinder B is
`$=20 * (27)/(8)$`

= 67.5
`mm^3`