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Question

A box with an open top has a square base and four sides of equal height. The volume of the box is 200 ftcubed. The height is 3 ft greater than both the length and the width. If the surface area is 185 ftsquared, what are the dimensions of the box?

find width and height

 

Answer 1

S is the side of the square base...

then the height H = s+3

V = 200 = s*s*(s+3)

200 = s^3 + 3s^2

0 = s^3 + 3s^2 - 200

Examining the graph of f(s) = s^3 + 3s^2 - 200,

the solution is s=5; Also, s=5 is in the set of potential

solutions , which does result in f(5)=0.

Then the height is 8.

the surface area is 2*lw + 2*lh + 2*hw = 2*5*5 + 2*5*8 + 2*5*8

= 50+80+80 = 210

BUT the top is missing, which has dimensions 5*5=25

so the surface area is 210-25 = 185.

Length=5

width=5

height=8