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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
10 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
10 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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