Given:
The length of Prism B is 3 times the length of Prism A. the width of Prism B is 4 times the width of Prism A. the height of Prism B is half of the height of Prism A.
Required:
We need to find the number of times the volume of Prism B is greater than Prism A.
Explanation:
Let l be the length of Prism A.
Let w be the width of Prism A.
Let h be the height of Prism A.
The length of Prism B is 3 times the length of Prism A
[tex]\text{ The length of Prism B =3l}[/tex]The width of Prism B is 4 times the width of Prism A.
[tex]\text{ The width of Prism B =3w}[/tex]The height of Prism B is half of the height of Prism A.
[tex]\text{ The height of Prism B =}\frac{1}{2}h[/tex]Consider the formula to find the value of the rectangular prism.
[tex]Volume\text{ = length }\times width\times height[/tex]Substitute known values to find the volume of A.
[tex]\text{ The volume of A=lwh}[/tex]Substitute known values in the formula to find the volume of B.
[tex]\text{ The volume of B=\lparen3l\rparen\lparen4w\rparen\lparen}\frac{1}{2}h)[/tex][tex]\text{ The volume of B=6lw}h[/tex][tex]Substitute\text{ the volume of A=lwh in the equation.}[/tex][tex]\text{ The volume of B=6 times the volume of A.}[/tex]Final answer:
[tex]\text{ The volume of prism B is 6 times greater than the volume of prism A.}[/tex]