Question

The dimensions of a rectangular prism are shown below length 1 1over2 width 1 foot hight 2 1over2

Answer 1

Given the dimensions of a rectangular prism as

length: 1.5 ft

width: 1 ft

Height: 2.5 ft

Part A.

Volume of a rectangular prism =

`\begin{gathered} V_(RP)=l* w* h \\ \\ l\text{ is the length} \\ \\ w\text{ is the width} \\ \\ h\text{ is the height} \end{gathered}`

`V_(RP)=1.5*1*2.5=3.75\text{ ft}^3`

Volume of small cubes

`V_(SC)=0.5^3=0.125\text{ ft}^3`

Number of small cubes that can be packed in a rectangular prism is 30

`N=(V_(RP))/(V_(SC))=(3.75)/(0.125)=30`

Hence, there are 30 small cubes that can be packed in the rectangular box.

Part B.

The volume is given as

`\sqrt[3]{30}=3.12`