92.131 Calculus 1 Optimization Problems 1)A Norman window has the outline of a semicircle on top of a rectangle as shown in the figure. Suppose there is π+8feet of wood trim available for all 4 sides of the rectangle and the semicircle. Find the dimensions of the rectangle (and hence the semicircle) that will maximize the area of the window. 2) You are building a cylindrical barrel in which to put Dr. Brent so you can float him over Niagara Falls. I can fit in a barrel with volume equal 1 cubic meter. The material for the lateral surface costs $18 per square meter. The material for the circular ends costs $9 per square meter. What are the exact radius and height of the barrel so that cost is minimized?3) A rectangular sheet of paper with perimeter 36 cm is to be rolled into a cylinder. What are the dimensions of the sheet that give the greatest volume?4) A right triangle whose hypotenuse is3 m long is revolved about one of its legs to generate a right circular cone. Find the radius, height, and volume of the cone of greatest volume.Note: hrV231π=. 5) Determine the cylinder with the largest volume that can be inscribed in a cone of height 8 cm and base radius 4 cm.3h r
has intentionally blurred sections.
Sign up to view the full version.