Question

Is it possible to find a value of $x$ so that the value of the surface area (in square inches) is equal to the value of the volume (in cubic inches)?
If possible, what is the value of $x$ ?
Write an equation to justify your answer.

Answer 1

The box has volume

11 in × 3 in × x in = 33x in³

and surface area

2 (11 in × 3 in + 11 in × x in + 3 in × x in) = (66 + 28x) in²

The volume and area have the same value if

33x = 66 + 28x

Solve this equation for x :

33x - 28x = 66

5x = 66

x = 66/5 = 13.2