Question

PLEASE HELP ME!

Answer 1

Answer:

A)  84 cubes

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

    $\sf Volume=3 \frac{1}{9}\:\:ft^3$

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:

$\sf Length=1 \frac{1}{3}\:ft=\dfrac{4}{3}\:ft=4\:thirds$

$\sf Width=1 \:ft=\dfrac{3}{3}\:ft=3\:thirds$

$\sf height=2 \frac{1}{3}\:ft=\dfrac{7}{3}\:ft=7\:thirds$

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:

$\textsf{Volume of small cube}=\sf \dfrac{1}{3} \times \dfrac{1}{3} \times \dfrac{1}{3}=\dfrac{1}{27}\:ft^3$

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

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

Answer 2

#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