Question

A rectangular prism has a length of 9 in., a width of 4 in., and a height of 1 1/2 in. The prism is filled with cubes that have edge lengths of 1/2 in. How many cubes are needed to fill the rectangular prism? Enter your answer in the box. To fill the rectangular prism, cubes are needed.

Answer 1

Volume of rectanglular prism

`\\ \rm\Rrightarrow LBH`

`\\ \rm\Rrightarrow 9(4)* 1(1)/(2)`

`\\ \rm\Rrightarrow 36* (3)/(2)`

`\\ \rm\Rrightarrow 18(3)`

`\\ \rm\Rrightarrow 54in^3`

Volume of each cube

`\\ \rm\Rrightarrow side^3`

`\\ \rm\Rrightarrow (1/2)^3`

`\\ \rm\Rrightarrow(1)/(8)in^3`

Total cubes

`\\ \rm\Rrightarrow (Volume\:of\:prism)/(volume\:of\:one\:cube)`

`\\ \rm\Rrightarrow 54/(1)/(8)`

`\\ \rm\Rrightarrow 54(8)`

`\\ \rm\Rrightarrow 432`

Answer 2

Answer: 432 cubes

Explanation: