Question

The dimensions of a rectangular prism are shown below. Length 1 1/3 feet Width 1 foot length 2 1/3 feet. The lengths of the sides of a small cube are 1/3 foot each. How many small cubes can be packed in the rectangular prism?

Answer 1

Answer:

84 cubes

Step-by-step explanation:

Given,

The dimension of the rectangular prism are,

$1\frac{1}{3}\text{ ft }\times 1\text{ ft }\times 2\frac{1}{3}\text{ ft }$

Hence, the volume of the prism,

$V=1\frac{1}{3}\times 1\times 2\frac{1}{3}$

$=\frac{4}{3}\times \frac{7}{3}$

$=\frac{28}{9}\text{ cube ft}$

Now, the volume of a cube = side³,

If side = $\frac{1}{3}$ ft,

Then the volume of each cube,

$V'=(\frac{1}{3})^3=\frac{1}{27}\text{ cube ft}$

Hence, the number of cubes that can be packet in the prism

$=\frac{V}{V'}$

$=\frac{28/9}{1/27}$

$=\frac{27\times 28}{9}$

$=3\times 28$

$=84$