Question

(Help with this Please?)

The dimensions of a rectangular prism are shown below:

Length: 1 1/2
Width: 1 foot
Height: 2 1/2
The lengths of the sides of a small cube are 1/2 foot each.


Part A: How many small cubes can be packed in the rectangular prism? Show your work. (5 points)

Part B: Use the answer obtained in part A to find the volume of the rectangular prism in terms of the small cube and a unit cube. (5 points)

Answer 1

30 cubes.

Explanation:

Answer 2

A) 30 cubes.

B) 30 units³.

Explanation:

A) 1. Calculate the volume of the rectangular prism, as following:

`Vr=(lenght)(width)(height)`

2. You have that:

- The length is:
`1^{(1)/(2)}ft=1.5ft`

- The width is:
`1ft`

- The heigth is:
`2^{(1)/(2)}ft=2.5ft`

3. Substitute these values into the formula:

`Vr=(1.5ft)(1ft)(2.5ft)=3.75ft^(3)`

4. The volume of one cube is:

`Vc=side^(3)`

5. The length of one side is:
`(1)/(2)ft=0.5ft`

6. Substitute this value into the formula:

`Vc=(0.5ft)^(3)=0.125ft^(3)`

7. The number of small cubes that can be packed in the rectangular prism is:

`cubes=(Vr)/(Vc)\\cubes=(3.75ft^(3))/(0.125ft^(3))\\cubes=30`

B) 1. The length, the width and the height of the rectangular prism in term of units cubes is:

`Length=(1.5ft)/(0.5ft)=3units`

`Width=(1ft)/(0.5ft)=2units`

`Heigth=(2.5ft)/(0.5ft)=5units`

2. Therefore, the volume of the rectagular prism in terms of the small cube and a unit cube is:

`Vr=(3units)(2units)(5units)=30units^(3)`