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If the base radius and the height of the cone is increased by 20%, by what percentage will the volume of the cone will increase.

If the base radius and the height of the cone is increased by 20%, by what percentage will the volume of the cone will increase.

Grade:10

2 Answers

Ajay Verma
askIITians Faculty 33 Points
9 years ago
soln::

volume of a cone = 1/3 (pi) * (radius)2*( height)
V = 1/3 (pi)* r2h
V = K r2h ; K = 1/3 (pi)

dv = k 2r * (dr)*h + k r2(dh)
dv/ v = 2 (dr/r) + dh/h

(dv/ v)* 100 = 2 (dr/r)*100 + (dh/h)*100

(dv/ v)* 100 = 2 * 20 + 20

= 60

so change in volume = 60%





Thanks and Regards,
Ajay verma,
askIITians faculty,
IIT HYDERABAD
Srishti Nanduri
38 Points
8 years ago
Thanks SIr for the answer. But the answer given in the book doesnt tally with your answer. The answer given in the book is 73%.

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