Question

How many cubes with edge length of ⅓ inch are needed to fill a rectangular prism that is 3 inches by 1 inch by 1 ⅓ inches?

Answer 1

We need 108 cubes to fill the rectangular prism

Explanation:

We are given the dimensions of a cube with an edge length of 1/3 inch.

A rectangular prism is to be filled out with those cubes. The dimensions of the prism are 3 inches x 1 inch x 1 1/3 inches.

The fraction 1 1/3 is expressed as:

`1(1)/(3)=1+(1)/(3)=(4)/(3)`

We need to know how many cubes fit in each dimension. It can be found by dividing them by their edge length:

`\displaystyle (3)/((1)/(3))=3*3 =9`

`\displaystyle (1)/((1)/(3))=1*3 =3`

`\displaystyle ((4)/(3))/((1)/(3))=(4)/(3)*3=4`

Now we multiply the number of cube per dimension:

9*3*4=108

We need 108 cubes to fill the rectangular prism