The formula for the volume of a rectangular box is V = l × w × h, where l is the length, w is the width, and h is the height. Since the density is given as 1 g/cm³, the mass of the object is equal to its volume in cubic centimeters (cc):
mass = volume × density
728 g = V × 1 g/cm³
V = 728 cm³
We are given the length and width of the box, so we can substitute these values into the formula for volume:
V = l × w × h
728 cm³ = 20.8 cm × 7 cm × h
Simplifying the right-hand side:
728 cm³ = 145.6 cm² × h
Dividing both sides by 145.6 cm²:
h = 728 cm³ ÷ 145.6 cm²
h = 5 cm
Therefore, the height of the box is 5 cm.