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k0ka [10]
3 years ago
11

It takes 154 cubes with side lengths of 1/2 inch to fill a rectangular prism. What is the volume of the rectangular prism? Show

your work or justify your solution.
Mathematics
1 answer:
Tju [1.3M]3 years ago
3 0

Answer:

The volume of the rectangular prism is <u>19.25 inches³</u>.

Step-by-step explanation:

Given:

It takes 154 cubes with side lengths of 1/2 inch to fill a rectangular prism.

Now, to find the rectangular prism's volume.

We first find the volume of a cube to fill in the rectangular prism.

The side length of the cube = \frac{1}{2}\ inch.

Now, to get the volume of cube we put formula:

Volume=(side)^3\\\\Volume=(\frac{1}{2})^3 \\\\Volume=\frac{1}{8}\ inch^3.

<em>Thus, the volume of a cube is  </em>\frac{1}{8} \ inch^3.<em />

<em>Number of cubes = 154.</em>

<u><em>According to question, it takes 154 cubes to fill the rectangular prism.</em></u>

<u><em>So, to get the volume of prism we need to find the volume of 154 cubes.</em></u>

Now, to get the volume of 154 such cubes we multiply the volume of a cube by number of cubes:

\frac{1}{8}\times 154\\\\ =\frac{154}{8}\\\\ =19.25\ inches^3.

Therefore, the volume of the rectangular prism is 19.25 inches³.

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