Question

On increasing the radii of the base and the height of a cone by 20%, its volume will increase by

Options

•  20%

•  40%

• 60%

• 72.8%

Answer 1

72.8%

Let the original radius of the cone be r and height be h.

Then, original volume`=1/3 pi"r"^2"h"`

`"Let"  1/3  pir^2"h" = V`

New radius = 120% of r

`=120/100`

`= (6r)/5`

New height = 120% of h 

`=(120"h")/100` 

`= (6"h")/ 5`

Hence, the new volume `= 1/3 pi xx((6"r")/5)^2xx"6h"/5`

`=216/125(1/3pi"r"^2"h")`

`=216/125 "V"`

Increase in Volume `= ((216)/(125)"v"-"V")`

`=(91"V")/(125)`

Increase in % of the volume `= ((991"V"))/125 xx 1/Vxx100)%`

`= 72.8 %`