Closed Calculus

[Ferocity]

Pa help ulit dito mga sir
"Find the volume of the largest right circular cylinder that can be cut from a circular cone of radius 6cm and 9cm.,"

 

[MoiGfx]

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[Arcturus]

maxima minima yan
Express the height in terms of the radius.

h = (3/2)(6 - r)

V = πr²h
V = πr²(3/2)(6 - r)
V = 9πr² - (3/2)πr³
dV/dr = 18πr - (9/2)πr²

Let dV/dr = 0
18πr - (9/2)πr² = 0
4r - r² = 0
r(4 - r) = 0
r = 4 ............... Reject r = 0.

V = πr²(3/2)(6 - r)
V = 48π cm³