Respuesta :
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:
Volume of a rectangular prism = ?
Solution:
Width of the prism = 3 cm
As given, height of a rectangular prism is half its width.
height of a rectangular prism = [tex]\frac{1}{2} \times3=\frac{3}{2} \ cm[/tex]
Similarly, as given, the width of the prism is 1/3 of its length.
Width of the prism = [tex]\frac{1}{3}\ of\ length[/tex]
[tex]3=\frac{1}{3}\times length[/tex]
By multiplying both sides by 3
[tex]3\times3=\frac{1}{3} \times3\ length\\9= length\\[/tex]
Thus, length of prism = 9 cm
Now, as we know:
[tex]Volume\ of\ rectangular\ prism=length\times breadth\times height[/tex]
[tex]=9\times3\times\frac{3}{2} \\\\ =\frac{81}{2} \\ \\ =40.5\ cm[/tex]
Therefore, the volume of a rectangular prism is 40.5 centimeters.
