Question

PLEASE HELP ME!

The dimensions of a rectangular prism are shown below:
Length: 1 1/3 feet
Width: 1 foot
Height: 2 1 /3 feet
The lengths of the sides of a small cube are 1 over 3 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.

Answer 1

#Part A

• L=1-1/3=4/3
• B=1
• H=2-1/3=7)3

Volume of rectanglular prism

• 4/3(1)(7/3)
• 28/9ft³

Volume of one cube

• side³
• (1/3)³
• 1/27in³

Total cubes

• 28/9÷1/27
• 28/9×27
• 28(3)
• 84cubes

#2

Volume=

No of cubes ×volume of 1 cube

• 84(1/27)
• 28/9in³

Answer 2

A) 84 cubes

B) Volume = 4 x 3 x 7 = 84 small cubes

`\sf Volume=3 (1)/(9)\:\:ft^3`

Explanation:

Part A

As the lengths of each side of the small cube are ¹/₃ ft each, to find the number cubes in the rectangular prism, first find how many thirds are in each dimension of the prism:

`\sf Length=1 (1)/(3)\:ft=(4)/(3)\:ft=4\:thirds`

`\sf Width=1 \:ft=(3)/(3)\:ft=3\:thirds`

`\sf height=2 (1)/(3)\:ft=(7)/(3)\:ft=7\:thirds`

Now simply multiply the number of thirds:

Number of cubes in prism = 4 x 3 x 7 = 84

Part B

As we have already found the dimensions of the prism in terms of the number of cubes, the volume of the prism in terms of the small cube is:

⇒ Volume = 4 x 3 x 7 = 84 small cubes

To find the volume of the prism in ft³, calculate the actual volume of the small cube:

`\textsf{Volume of small cube}=\sf (1)/(3) * (1)/(3) * (1)/(3)=(1)/(27)\:ft^3`

Now multiply the volume in terms of number of cubes by the actual volume of a cube:

`\begin{aligned}\textsf{Volume} &= \sf \textsf{Volume in cubes} * \textsf{Volume of cube in ft}^3\\\\& = \sf 84 * (1)/(27)\:ft^3\\\\& =\sf (84)/(27)\:ft^3\\\\& =\sf 3(1)/(9)\:ft^3\end{aligned}`