Question

what is the volume of the rectangular prism? type the answer in the boxes below.
image of a small cube labeled \\(\frac{1}{2}\\) cm and a rectangular prism made of such cubes
input box with \\(\frac{\quad}{\quad}\\) cm³ format

Explanation:

Step1: Determine the number of cubes along each edge

Looking at the rectangular prism, we can see that along the length, there are 5 small cubes, along the width, there are 2 small cubes, and along the height, there are 3 small cubes.

Step2: Calculate the volume of one small cube

The side length of each small cube is $\frac{1}{2}$ cm. The volume of a cube is given by $V = s^3$, where $s$ is the side length. So the volume of one small cube is $(\frac{1}{2})^3=\frac{1}{8}$ $cm^3$.

Step3: Calculate the total number of small cubes

To find the total number of small cubes in the rectangular prism, we multiply the number of cubes along each edge: $5\times2\times3 = 30$.

Step4: Calculate the volume of the rectangular prism

The volume of the rectangular prism is the number of small cubes times the volume of one small cube. So we have $30\times\frac{1}{8}=\frac{30}{8}=\frac{15}{4}$ (or we can also calculate it by finding the length, width, and height of the prism in terms of the side length of the small cube. The length of the prism is $5\times\frac{1}{2}=\frac{5}{2}$ cm, the width is $2\times\frac{1}{2} = 1$ cm, and the height is $3\times\frac{1}{2}=\frac{3}{2}$ cm. Then the volume $V=l\times w\times h=\frac{5}{2}\times1\times\frac{3}{2}=\frac{15}{4}$ $cm^3$).

Answer:

$\frac{15}{4}$