Question

A packaging firm has been hired to create a box for baby blocks. The firm was hired because it could save money by creating a box using the least amount of material. the packaging firm knows that the volume of the box must be 18cm^3.

A. What are the possible dimensions for the box if the volume must be18 cm3?

B . Which set of dimensions should the package firm choose in order to use the least amount of material? Explain Please show work

Answer 1

A. 3cm by 3cm by 2cm or 6cm by 3cm by 1cm

B. 3cm by 3cm by 2cm

Explanation:

POSSIBLE DEMENSIONS

3cm by 3cm by 2cm = 18cm^3

6cm by 3cm by 1cm = 18cm^3

LEAST AMOUNT OF MATERIAL

3 by 3 by 2 would mean 6cm squared of material per side

6 + 6 + 6 + 6 + 6 + 6 = 6 times 6 = 36

Total : 6 sides = 36cm^2 used

6 by 3 by 1 would mean 2 sides of 6cm^2, 2 sides of 3cm^2 and 2 sides of 18cm^2

18 + (6 + 6) + (3 + 3) =

18 + 12 + 9 =

30 + 9 = 39

Total: 39cm^2