Question 882692
The volume, {{{V}}} , of a cone with radius {{{r}}} and height {{{h}}} is calculated as
{{{V=(1/3)(pi*r^2)*h}}}
In that expression, {{{pi*r^2}}} is the area of the base of the cone.
 
If the radius is quadrupled, the new radius would be {{{4r}}} .
Then, the area of the base would be {{{pi*(4r^2)=pi*4^2*r^3=pi*16*r^2=16*(pi*r^2)}}} , and that would be {{{16}}} times more area for the base.
 
If the height is reduced to {{{1/5}}} of the original height, the new height would be {{{(1/5)*h}}} .
 
If the radius is quadrupled, and the height is reduced to {{{1/5}}} of the original height, the new cone volume will be
{{{(1/3)*(pi*(4r)^2)*((1/5)*h)=(1/3)(16*(pi*r^2))*((1/5)*h)=(1/3)*16*(pi*r^2)*(1/5)*h=(16*(1/5))*(1/3)(pi*r^2)*h=(16/5)*(1/3)(pi*r^2)*h=(16/5)*V}}}
That is {{{16/5}}} of the original cone's volume.