Question

A right Circular Cone is enveloping a right cylinder such that the base of the cylinder rest on the base of the cone. If the radius and the height of the cone is 4 cm and 10 cm respectively ,then the largest possible curved surface area of the cylinder of the radius 'r'

Answer 1

Radius= r = PE
AP= h
PQ= (10-h)
since ΔAPE is congurent to ΔAQC
AP/AQ = PE/QC

h/10= r/4
h= 10r/4

putting the value in above equation of PQ
PQ= 10 - 10r/4

=10 - 5r/2

curve surface area of cylinder= 2pie r (10 - 5r/2)

=pie r (20- 5r)
r=5 pie r ( 4-r)

Answer 2

Answer:

5pie r (4-r)

Step-by-step explanation:

Radius= r = PE

AP= h

PQ= (10-h)

since ΔAPE is congurent to ΔAQC

AP/AQ = PE/QC

h/10= r/4

h= 10r/4

putting the value in above equation of PQ

PQ= 10 - 10r/4

=10 - 5r/2

curve surface area of cylinder= 2pie r (10 - 5r/2)

=pie r (20- 5r)

r=5 pie r ( 4-r)

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