A rectangular box has a square base. Its height is one third the width of the base. Find a function that models its volume V in terms of its width w.

Question

 A rectangular box has a square base. Its height is one third the width of the base. Find a function that models its volume V in terms of its width w.

Answer 1

Michael,

 

Volume equals length x width x height.  In this case, you are told the base is square, which means two of the measurements are the same, lets call them x.  You are further told that the height is 1/3 the width of the base, which we already defined as x.  So the height is 1/3x.

 

Therefore, the volume is x * x * 1/3x.

 

Written as a function, f(x)=1/3x³

 

I hope that helps,

 

Norm.

Answer 2

I assume w that you are referring to is one side of the base square.

 

Volume of a rectangle = V = Base area * height

= w * w * (1/3) w = 1/3 w^3