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

Question

KollegeApply · Accepted Answer

72.8% Let the original radius of the cone be r and height be h. Then, original volume=$\frac{1}{3}$ pi"r"^2"h" "Let" $\frac{1}{3}$ pir^2"h" = V New radius = 120% of r =$\frac{120}{100}$ = (6r)/5 New height = 120% of h =(120"h")/100 = (6"h")/ 5 Hence, the new volume `= $\frac{1}{3}$ pi xx((6"r")/5)^2xx"6h"/5 =$\frac{216}{125}$($\frac{1}{3}$pi"r"^2"h") =$\frac{216}{125}$ "V" Increase in Volume = ((216)/(125)"v"-"V") =(91"V")/(125)` Increase in % of the volume `= ((991"V"))/125 xx 1/Vxx100)% = 72.8 %`

AChoose Your Answer