Mar wants to make a box with no lid from a rectangular sheet of cardboard that is 18 inches by 24 inches. The box is to be made by cutting a square of side x from each corner of the sheet and folding up the sides. Find the value of x that maximizes the volume of the box.

A.   4.3 inches C.   10.6 inches
B.   5.2 inches D.   3.4 inches


Problem 310 - 311 | Equilibrium of Concurrent Force System

Required Force to Hold the Box in a Smooth Plane - Equilibrium of Force System

Problem 310
A 300-lb box is held at rest on a smooth plane by a force P inclined at an angle θ with the plane as shown in Fig. P-310. If θ = 45°, determine the value of P and the normal pressure N exerted by the plane.

Block supported by a force in the incline


245 - Couple in the box

Problem 245
Refer to Fig. 2-24a. A couple consists of two vertical forces of 60 lb each. One force acts up through A and the other acts down through D. Transform the couple into an equivalent couple having horizontal forces acting through E and F.



007 Components of a force parallel and perpendicular to the incline

Problem 007
A block is resting on an incline of slope 5:12 as shown in Fig. P-007. It is subjected to a force F = 500 N on a slope of 3:4. Determine the components of F parallel and perpendicular to the incline.

Box resting on the incline


56 - 57 Maxima and minima problems of square box and silo

Problem 56
The base of a covered box is a square. The bottom and back are made of pine, the remainder of oak. If oak is m times as expensive as pine, find the most economical proportion.

29 - 31 Solved problems in maxima and minima

Problem 29
The sum of the length and girth of a container of square cross section is a inches. Find the maximum volume.

25 - 27 Solved problems in maxima and minima

Problem 25
Find the most economical proportions of a quart can.

21 - 24 Solved problems in maxima and minima

Problem 21
Find the rectangle of maximum perimeter inscribed in a given circle.

15 - 17 Box open at the top in maxima and minima

Problem 15
A box is to be made of a piece of cardboard 9 inches square by cutting equal squares out of the corners and turning up the sides. Find the volume of the largest box that can be made in this way.

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