Question

A box with a square base and top is made with a cardboard that costs 0.3 cents per cm² . The base is double layered for reinforcement. If the total cost for material is fixed at 3.6 dollars, what is the dimensions of the box that maximizes the volume? Enter the exact values (i.e., no approximation).

Answer 1

Length = 10 cm

Width = 10 cm

Height = 12 cm

Explanation:

Cost of a cardboard with a square base and top = 0.3 cents per cm²

0.3 cents = $0.003 (0.3/100)

Total cost for material = $3.6

The volume of the box = $3.6/$0.003 = 1,200cm³

The formula for volume = length × width × height.

Since the base and top are square, the length and width must have equal sizes.

Let us assume that

length = 10cm

width = 10cm

these will give an area of 100cm².

Volume = length * width * height

= Area * height

= 10 * 10 * height

= 100cm² * height

Therefore, the height will be the volume divided by area

= 1,200cm³/100cm²

= 12cm

Volume = 10 * 10 * 12

= 1,200cm³