Question

Jada is using 84 one-centimeter cubes to build a rectangular prism. She wants the height of the rectangular prism to be 4 centimeters. She also wants the width to be shorter than the length. How many rectangular prisms with different dimensions could Jada build

Answer 1

One rectangular prism is possible with 7cm × 3cm × 4cm.

Explanation:

Jada used number of cubes = 84

Side of one small cube = 1 cm

Volume of one small cube = 1 cm³

Volume of 84 small cubes = 84 cm³

She wants to build a rectangular prism with height = 4 cm

Let the length of the prism = x cm

and the width of the prism = y cm

and x > y

Volume of the prism = length × width × height

= (x)(y)(4)

= 4xy cm³

If the volume of prism = volume of 84 small cubes

Then 4xy = 84

xy = 21

Possible values of x = 3, 7

and y = 7, 3

But x > y

So x = 7 and y = 3 will be the answer.

Therefore, only one rectangular prism is possible with dimensions

length = 7 cm, width = 3 cm, height = 4 cm.