Question 23

In Exercise 87 in Section 2.1, you numerically and graphically found the dimensions that would produce a maximum enclosed area. Use calculus to determine analytically the dimensions that should be used so that the enclosed area will be a maximum. 23. Maximum Volume (a) Verify that each of the rectangular solids shown in the figure has a surface area of 150 square inches. (b) Find the volume of each solid. (c) Determine the dimensions of a rectangular solid (with a square base) of maximum volume if its surface area is 150 square inches. 3.25 24. Maximum Volume Determine the dimensions of a rectangular solid (with a square base) with maximum volume if its surface area is 337.5 square centimeters. 25. Maximum Area A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window (see figure). Find the dimensions of a Norman window of maximum area if the total perimeter is 16 feet