Question

The height and radius of a right circular cone are increased by 20%and 25% respectively. Find the ratio of the volume of new cone and old cone.

Answer 1

Let for old cone,
height = h
and radius = r
Volume `V_(1)=(1)/(3)pi r^(2)h`
For new cone,
Increase in height = 20% of `h=hxx(20)/(100)=(h)/(5)`
`therefore` Height `H=h+(h)/(5)=(6h)/(5)`
Increase in radius = 25% of `r=r xx (25)/(100)=(r )/(4)`
`therefore` Radius `R = r+(r )/(4)=(5r)/(4)`
Now, volume `V_(2)=(1)/(3)pi R^(2)H=(1)/(3)pi ((5pi)/(4))^(2).((6h)/(5))=(1)/(3)pi r^(2)h. (15)/(8)`
The ratio of volume `=("Volume of new cone")/("Volume of old cone")=(V_(2))/(V_(1))=((1)/(3)pi r^(2)h.(15)/(8))/((1)/(3)pi r^(2)h)=(15)/(8)=15 : 8`