sloaneetkennedy
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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.

Sagot :

#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
semsee45

Answer:

A)  84 cubes

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

    [tex]\sf Volume=3 \frac{1}{9}\:\:ft^3[/tex]

Step-by-step 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:

[tex]\sf Length=1 \frac{1}{3}\:ft=\dfrac{4}{3}\:ft=4\:thirds[/tex]

[tex]\sf Width=1 \:ft=\dfrac{3}{3}\:ft=3\:thirds[/tex]

[tex]\sf height=2 \frac{1}{3}\:ft=\dfrac{7}{3}\:ft=7\:thirds[/tex]

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:

[tex]\textsf{Volume of small cube}=\sf \dfrac{1}{3} \times \dfrac{1}{3} \times \dfrac{1}{3}=\dfrac{1}{27}\:ft^3[/tex]

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

[tex]\begin{aligned}\textsf{Volume} &= \sf \textsf{Volume in cubes} \times \textsf{Volume of cube in ft}^3\\\\& = \sf 84 \times \dfrac{1}{27}\:ft^3\\\\& =\sf \dfrac{84}{27}\:ft^3\\\\& =\sf 3\frac{1}{9}\:ft^3\end{aligned}[/tex]

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