On Increasing the Radii of the Base and the Height of a Cone by 20%, Its Volume Will Increase by - Mathematics

MCQ

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

•  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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APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 19 Volume and Surface Area of Solids
Multiple Choice Questions | Q 60 | Page 923