Answer:
40.5 centimeters.
Step-by-step explanation:
Given:
The width of the prism is 3 centimeters.
The width of the prism is 1/3 of its length.
The height of a rectangular prism is half its width.
To find:
<u>Volume of a rectangular prism = ?</u>
Solution:
Width of the prism = 3 cm
As given, height of a rectangular prism is half its width.
height of a rectangular prism = ![\frac{1}{2} \times3=\frac{3}{2} \ cm](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes3%3D%5Cfrac%7B3%7D%7B2%7D%20%5C%20cm)
Similarly, as given, the width of the prism is 1/3 of its length.
Width of the prism = ![\frac{1}{3}\ of\ length](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%5C%20%20of%5C%20length)
![3=\frac{1}{3}\times length](https://tex.z-dn.net/?f=3%3D%5Cfrac%7B1%7D%7B3%7D%5Ctimes%20length)
By multiplying both sides by 3
![3\times3=\frac{1}{3} \times3\ length\\9= length\\](https://tex.z-dn.net/?f=3%5Ctimes3%3D%5Cfrac%7B1%7D%7B3%7D%20%5Ctimes3%5C%20length%5C%5C9%3D%20length%5C%5C)
Thus, length of prism = 9 cm
Now, as we know:
![Volume\ of\ rectangular\ prism=length\times breadth\times height](https://tex.z-dn.net/?f=Volume%5C%20of%5C%20rectangular%5C%20prism%3Dlength%5Ctimes%20breadth%5Ctimes%20height)
![=9\times3\times\frac{3}{2} \\\\ =\frac{81}{2} \\ \\ =40.5\ cm](https://tex.z-dn.net/?f=%3D9%5Ctimes3%5Ctimes%5Cfrac%7B3%7D%7B2%7D%20%5C%5C%5C%5C%20%3D%5Cfrac%7B81%7D%7B2%7D%20%5C%5C%20%5C%5C%20%3D40.5%5C%20cm)
Therefore, the volume of a rectangular prism is 40.5 centimeters.