Question

Design a closed rectangular box of width w, length l, and height h. The sides of the box cost 1 cent/cm2 and the top and bottom cost 2 cent/cm2 . (a) Write an equation for cost (in cents) in terms of w, l, and h. Use lower case letters.

Answer 1

Equation for cost (in cents) in terms of w, l, and h is 2h(w + l) + 4l*w

Explanation:

We are given

A rectangular box with dimensions

Width = w

Length = l

Height = h

This needs to be visualized in 3D

First type of Sides of the box is made using the width and height

second type is made using length and height

Area of the 1st two sides = 2*w*h

Area of the 2nd type of sides = 2*l*h

Area of the top and bottom = 2*l*w

Cost for sides = 1cent/cm^2

Cost of the sides calculated = cost* Area= 1*(2*w*h+2*l*h)

= 2h(w + l)

similarly

cost of top and bottom = 2*2*l*w = 4*l*w

Total Cost = 2h(w + l) + 4l*w