Question

A right rectangular prism has these dimensions:

Length: Fraction 1 and 1 over 2 units
Width: Fraction 1 over 2 unit
Height: Fraction 3 over 4 unit

How many cubes of side length Fraction 1 over 4 unit are required to completely pack the prism without any gap or overlap?

36
45
51
60

Answer 1

Answer:36

Explanation:

Answer 2

Hey there :)

The volume formula of a rectangular prism is
V = height x length x width

Given are:
Length =
`1(1)/(2) = (3)/(2)`
Width =
`(1)/(2)`
Height =
`(3)/(4)`

Lets find the volume:
V =
`(3)/(2)` x
`(1)/(2)` x
`(3)/(4)`
=
`(9)/(16)` units³

The volume formula of a cube is
V = side³

Given is:
Side =
`( (1)/(4) )^3`
=
`(1)/(64)` units³

To find how many cubes fit in the rectangular prism, we divide the volumes
Volume of prism divided by volume of cube

`(9)/(16)` ÷
`(1)/(64)`
Since it is a fraction that is involved in division, we find the reciprocal and multiply

=
`(9)/(16)` x 64
= 36

Your answer will be the 1st option