Question

Describe how multiplying all the linear dimensions of a cone by one

fourth affects the volume of the solid. *

Answer 1

Answer:
`(1)/(64)^(th)`

Explanation:

Given

Suppose V is the original volume of cone having r as radius and h as height

If we multiply all the linear dimensions of ac one by
`(1)/(4)^(th)`

the
`r'=(r)/(4)`

`h'=(h)/(4)`

Therefore new volume is

`V'=(1)/(3)\pi r'^2h'`

`V'=(1)/(3)\pi ((r)/(4))^2((h)/(4))`

`V'=(1)/(64)* (1)/(3)\pi r^2h`

`V'=(V)/(64)`

So new volume becomes
`(1)/(64)^(th)` of the original one