the large solid below is made from small cubes. each has a side length of $\frac{1}{3}$ cm. answer the…
the large solid below is made from small cubes. each has a side length of $\frac{1}{3}$ 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? $square$ cm$^{3}$ (c) what is the volume of the large solid? $square$ cm$^{3}$
Answer
Explanation:
Step1: Count small - cubes in each dimension
The large cube has 3 small - cubes along each edge. So the total number of small cubes is $3\times3\times3 = 27$.
Step2: Calculate volume of a small cube
The volume formula for a cube is $V = s^3$, where $s$ is the side - length. Given $s=\frac{1}{3}$ cm, then $V=\left(\frac{1}{3}\right)^3=\frac{1}{27}$ $cm^3$.
Step3: Calculate volume of the large solid
The volume of the large solid is the number of small cubes times the volume of one small cube. Since there are 27 small cubes and each has a volume of $\frac{1}{27}$ $cm^3$, the volume of the large solid is $27\times\frac{1}{27}=1$ $cm^3$.
Answer:
(a) 27 (b) $\frac{1}{27}$ (c) 1