Question

If the sum of diameter and height of a cone is 10 cm, what will be radius of the cone when the volume is maximum?

a.3.33 cm

b.5 cm

c.6.66 cm

d.7 cm

Answer 1

5.............................................

Answer 2

Answer:

condition:

D+h=10

2r+h=10

h=10-2r

volume of cone= (1/3)*πr^ 2h

=(1/3)*πr^2(10-2r)

v=(10/3)*πr^2 -(2/3)*πr^3

dv/dr = (20/3)πr-2πr

when volume is maximum, dv/dr =0

dv/dr =(20/3)πr-2πr=0

(20/3)πr= 2πr

r= 3.33 cm