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A prism is completely filled with 2304 cubes that have edge length of 1/4 cm


What is the volume of the prism?


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Verified Answer :

The volume of the prism is 233.

Answer:

\(36\text{ cm}^3\)

Step-by-step explanation:

We have been given that a prism is completely filled with 2304 cubes that have edge length of 1/4 cm.

This means that volume of prism will be equal to the volume of 2304 cubes. First of all let us find the volume of each cube using volume of cube formula.

\(\text{Volume of cube}=a^3\), where a represents the length of each edge.

Upon substituting our given values in volume formula we will get,

\(\text{Volume of the cube}=(\frac{1}{4}\text{ cm})^3\)

\(\text{Volume of the cube}=\frac{1^3}{4^3}\text{ cm}^3\)

\(\text{Volume of the cube}=\frac{1}{64}\text{ cm}^3\)

\(\text{Volume of prism}=2304\times\frac{1}{64}\text{ cm}^3\)

\(\text{Volume of prism}=36\text{ cm}^3\)

Therefore, the volume of our given prism is 36 cubic cm.

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