Question

A rectangular prism with a volume of 8 cubic units is filled with cubes twice: once with cubes with side lengths of 1/2 unit and once with cubes with side lengths of 1/3 unit. How many more of the 1/3-unit cubes are needed to fill the prism than if we used the 1/2-unit cubes? * Your answer

Answer 1

Explanation:

Given that,

A rectangular prism with a volume of 8 cubic units, V = 8 cubic units

The rectangular prism is filled with a cube twice.

First one

A cube with ½ length unit, we should know that a cube have equal length

Then, L = ½ units

Volume of a cube is L³

V = L³

V1 = (½)³ = ⅛ cubic units

Second cube

A cube with ⅓ length unit, we should know that a cube have equal length

Then, L = ⅓ units

Volume of a cube is L³

V = L³

V1 = (⅓)³ = 1 / 27 cubic units

So, to know number of times cube one will filled the rectangular prism

V = nV1

Where V is the volume of rectangular prism

n is the number of times the cube will be able to matched up with the volume of the rectangular prism

Then, n_1 = V / V1

n_1 = 8 / ⅛

n_1 = 64 times

Also,

n_2 = V / V2

n_2 = 8 / 1 / 27

n_2 = 8 × 27 = 216 times

So, the we need more of ⅓units and we will need (216 - 64) = 152 times

We need 152 more of ⅓units