Question

1. The edge lengths of a right rectangular prism are

1/2 meter, 1/2 meter, and 3/4 meter. How many unit cubes with edge lengths of 1/12 meter can fit inside?

Someone please help me. I dont understand this at all, so I can't give you my answer. If anyone could simplify the question or give me the answer so I can put it into my own words, that would be great. Thanks

Answer 1

324 cubes.

Explanation:

Let n be the number of cubes with edge length 1/12 meter.

We have been given the lengths of edges of a right rectangular prism as
`(1)/(2)` meter,
`(1)/(2)` meter and
`(3)/(4)` meter.

`\text{Volume of rectangular prism}=L*B*H`, where,

L = Length of prism,

B = Breadth of prism,

H = Height of prism.

`\text{Volume of cube}=a^3`, where a= length of each edge of the cube.

The volume of n cubes with each edge 1/12 will be equal to the volume of rectangular prism.

`\text{Volume of n cubes}=\text{Volume of rectangular prism}`

`n* a^3=L*B*H`

Upon substituting our given values we will get,

`n*((1)/(12))^3=(1)/(2)* (1)/(2)* (3)/(4)`

`n*(1^3)/(12^3)=(1*1*3)/(2*2*4)`

`n*(1)/(1728)=(3)/(16)`

Let us multiply both sides of our equation by 1728.

`(n)/(1728)*1728=(3)/(16)*1728`

`n=(3)/(16)*1728`

`n=3*108`

`n=324`

Therefore, 324 unit cubes can fit inside the given right rectangular prism.