Cylinder
Cylinder
What are the dimensions of such a cylinder which has maximum volume?
A cylinder is inscribed in a right circular cone of height 2 and radius (at the base) equal to 4.5. What are the dimensions of such a cylinder which has maximum volume?
Radius =
Height =
How would I solve this question?
Thank you!
The slope of the cone's side is 2/4.5
The volume of the cylinder is pi x r^2 x h
From the edge of the cone to the cylinder base is ( 4.5 - r ) and the slope is h / (4.5 - r) = 2 / 4.5
So h = 2(4.5 - r) / 4.5
Thus, the volume of the cylinder is pi x r^2 x 2(4.5 - r) / 4.5 = 2pi (r^2 - r^3/4.5)
Find dV/dr = 0 dV/dr = 2 pi (2r - 3 r^2/4.5) = 0 ==> 2r = 3r^2/4.5 ==> 9 = 3r ==> r = 3
Radius = 3
h = 2(4.5 - 3) / 4.5 = 3 / 4.5 = 1 / 1.5 = 2 / 3 = 0.667
Height = 0.667
Making Worthing Steel Scuba Cylinders
Cylinder
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September 18th, 2011 in
Uncategorized | tags: cylinder, cylinder and slide, cylinder head, cylinder seals, cylinder surface area, cylinder vases, cylinder volume, cylinder volume calculator, cylinder volume formula, cylinder works