The volume as a function of the location of that vertex is
... v(x, y, z) = x·y·z = x·y·(100-x²-y²)
This function is symmetrical in x and y, so will be a maximum when x=y. That is, you wish to maximize the function
... v(x) = x²(100 -2x²) = 2x²(50-x²)
This is a quadratic in x² that has zeros at x²=0 and x²=50. It will have a maximum halfway between those zeros, at x²=25. That maximum volume is
... v(5) = 2·25·(50-25) = 1250
The maximum volume of the box is 1250 cubic units.
Answer:
The radius of this circle is and the central angle of the sector is
.
Step-by-step explanation:
Consider the provided information.
If a conical paper funnel is made out of a sector of circle then the radius of the sector becomes the slant height of the cone, and the length of the curved part of the sector becomes the circumference of the base of the cone.
First find the slant height:
Thus, the radius of the sector is which is same as the slant height of the cone.
Now, the circumference of the base of the cone is same as the length of the curved part.
The length of the curved part =
Hence, the radius of this circle is and the central angle of the sector is
.