Question

PLEASE ANSWER!

A cylinder has a volume of 216 cm3. By what factor must the dimension of the cylinder be multiplied to give a similar cylinder and reduce the volume by 208 cm3

Answer 1

Dimensions of cylinder must be multiplied by a factor of
`\frac {1} {3}`, to give a similar cylinder and reduce the volume by 208
`cm^3`.

Explanation:

Here we have , A cylinder has a volume of 216
`cm^3`. By what factor must the dimension of the cylinder be multiplied to give a similar cylinder and reduce the volume by 208
`cm^3` . Let's find out:

We know that Volume of cylinder =
`\pi r^2h`

Now , Similar cylinder means dimensions are in same ratio . According to question initial volume is 216
`cm^3` i.e.

⇒
`V =216 = \pi r^2h`

Now , the volume is reduced by 208
`cm^3` , So new volume is :

⇒
`V_1=216-208`

⇒
`V_1=8=\pi r_1^2h_1`

Here ,
`(V)/(V_1) = (r^2h)/(r_1^2h_1)`

⇒
`(216)/(8) = (r^2h)/(r_1^2h_1)`

⇒
`27= (r^2h)/(r_1^2h_1)`

⇒
`r_1^2h_1= (r^2h)/(27)`

⇒
`r_1^2h_1= ((r)/(3))^2(h)/(3)`

Therefore , Dimensions of cylinder must be multiplied by a factor of
`\frac {1} {3}`, to give a similar cylinder and reduce the volume by 208
`cm^3`