Question

the large solid below is made from small cubes. each has a side length of $\frac{1}{5}$ cm. 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? cm³ (c) what is the volume of the large solid? cm³

Explanation:

Step1: Count the number of small - cubes in length, width and height

The large solid has length with 5 small - cubes, width with 3 small - cubes and height with 2 small - cubes.

Step2: Calculate the number of small cubes

The number of small cubes $n$ in the large solid is found by multiplying the number of small cubes in each dimension. So $n = 5\times3\times2=30$.

Step3: Calculate the volume of one small cube

The volume $V_{small}$ of a cube is given by the formula $V = s^3$, where $s=\frac{1}{5}$ cm. So $V_{small}=(\frac{1}{5})^3=\frac{1}{125}$ $cm^3$.

Step4: Calculate the volume of the large solid

The volume $V_{large}$ of the large solid is the number of small cubes times the volume of one small cube. Since $n = 30$ and $V_{small}=\frac{1}{125}$ $cm^3$, then $V_{large}=30\times\frac{1}{125}=\frac{30}{125}=\frac{6}{25}$ $cm^3$.

Answer:

(a) 30
(b) $\frac{1}{125}$
(c) $\frac{6}{25}$