Question

Alex has 64 cubes, with the dimensions in ft (1/2) he uses all the cubes to fill a box shaped like a larger rectangular prism. there are no gaps between the cubes.

A. what is the volume, in cubic feet, of the larger rectangular prism?


B. what is the possible set of dimensions , in feet, of the larger rectangular prism?

A. Volume:

B. Length:

Width:

Height:

Answer 1

A. 8 square feet
B. Length, 1ft. Width 1 ft Height 8ft
A. to find the volume you can multiply the dimensions (0.5 *0.5*0.5) by the total amount of cubes. 0.5*0.5*0.5* 64 = 8 sq feet.
B. to create dimensions I used factors of 8. 8/2 = 4. 4*2*1 = 8

Answer 2

A) First, find the volume of each cube:
V = s³
= (1/2)³
= 1/8 ft³

We have a total of 64 cubes, therefore the maximum volume will be:
Vmax = 64 · (1/8) = 8 ft³

B) The volume of a rectangular prism is given by:
V = w × l × h
Therefore any combination of w × l × h = Vmax = 8 will be fine.
Examples:
2 × 2 × 2
4 × 2 × 1