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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%
Solution
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 %`
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