Question

the large solid below is made from small cubes. each has a side length of $\frac{1}{4}$ m. answer the questions below. write your answers in simplest form. (a) how many small cubes is the large solid made of? (b) what is the volume of one of the small cubes? $square m^{3}$ (c) what is the volume of the large solid? $square m^{3}$

Explanation:

Step1: Count small - cubes in dimensions

Count the number of small cubes along length, width, and height. The length has 8 small - cubes, the width has 3 small - cubes, and the height has 3 small - cubes.
The total number of small cubes $n=8\times3\times3 = 72$.

Step2: Calculate volume of small cube

The volume formula for a cube is $V = s^3$, where $s$ is the side - length. Given $s=\frac{1}{4}$ m, then $V_{small}=(\frac{1}{4})^3=\frac{1}{64}$ m³.

Step3: Calculate volume of large solid

The volume of the large solid is the number of small cubes times the volume of one small cube. Since $n = 72$ and $V_{small}=\frac{1}{64}$ m³, then $V_{large}=72\times\frac{1}{64}=\frac{72}{64}=\frac{9}{8}$ m³.

Answer:

(a) 72
(b) $\frac{1}{64}$
(c) $\frac{9}{8}$