Question

How many cubes with side lengths of 1/3 does it take to fill the prism?

Answer 1

Answer:

180 cubes

Step-by-step explanation:

little cubes:

$v=(\frac{1}{3} )^{3} =\frac{1}{27}$

The prism:

$v=(\frac{5}{3})(\frac{4}{3} )(2)=\frac{40}{9} =\frac{20}{3}$

the number of cubes that fill the prism:

$cubes=\frac{\frac{20}{3} }{\frac{1}{27} } =\frac{(20)(27)}{(3)(1)}= \frac{540}{3} =180$

Hope this helps

Answer 2

Total 120 cubes will required to fill the prism.

What is volume?

" Volume is defined as total space occupied by any three dimensional object enclosed on it."

Formula used

Volume of prism = Area of the base × height

Volume of the cube = ( side length)³

According to the question,

Side length of cube = 1 / 3cm

Length of the base of the prism = 5 / 3cm

Width of the base of the prism = 4 / 3cm

height of the prism = 2cm

Substitute the value in the formula we get,

Volume of the cube = ( 1 / 3)³

                                 = (1 / 27)cm³

Area of the base of the prism = ( 5 / 3) × ( 4 / 3)

                                                 = (20 / 9) cm²

Volume of the prism = (20 / 9) × 2

                                  = ( 40 / 9) cm³

Number of cubes required to fill the prism = (40 / 9) / ( 1 /27)

                                                                       = (40 × 27) / 9

                                                                       = 120 cubes

Hence, total 120 cubes will required to fill the prism.

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