# Box

**Problem**

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

**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.

## 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.

## 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.