Question

Describe how multiplying all the linear dimensions of a cone by one
fourth affects the volume of the solid. *

Answer 1

Answer:$\frac{1}{64}^{th}$

Step-by-step 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 $\frac{1}{4}^{th}$

the $r'=\frac{r}{4}$

$h'=\frac{h}{4}$

Therefore new volume is

$V'=\frac{1}{3}\pi r'^2h'$

$V'=\frac{1}{3}\pi (\frac{r}{4})^2(\frac{h}{4})$

$V'=\frac{1}{64}\times \frac{1}{3}\pi r^2h$

$V'=\frac{V}{64}$

So new volume becomes $\frac{1}{64}^{th}$ of the original one