A cylinder is inscribed in a right circular cone of height 2 and radius (at the base) equal to 2. What are the dimensions of such a cylinder which has maximum volume?

Question

anonymous · Answer

calculus

anonymous · Answer

This is an answer for a radius of 6... just substitute your 2 for the 6

The radius of the inscribed cylinder at height x is given as (6/2 * (2-x))
so V = pi* (6/2 * (2-x))^2 * x
dV/dx = 0 = (2-x)^2*3+3x(2(2-x)(-1))
3(2-x)^2=6x(2-x)
2-x = 2x
3x = 2
x = 2/3
so the cylinder has a height of 2/3 and radius of (6/2 * (2-x)) = 4

anonymous · Answer

apparently the radius is wrong :/

anonymous · Answer

do your own hw, stop asking people to do it for you