a cone is constructed by cutting a sector from a circular sheet of metal with radius . the cut sheet is then folded up and welde
d. find the radius and height of the cone with maximum volume that can be formed in this way.
1 answer:
The expression for the radius and height of the cone can be obtained from
the property of a function at the maximum point.
- The height of the cone is half the length of the radius of the circular sheet metal.
Reasons:
The part used to form the cone = A sector of a circle
The length of the arc of the sector = The perimeter of the circle formed by the base of the cone.

θ/360·2·π·s = 2·π·r
Where;
s = The radius of he circular sheet metal
h = s² - r²
3·r²·s² - 4·r⁴ = 0
3·r²·s² = 4·r⁴
3·s² = 4·r²


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