∴ Volume of rectangular prism is [tex]192in^{3}[/tex] & Volume of cube is [tex]1in^{3}[/tex] and , cubes with edge lengths of 1 inch would be needed to fill the prism is 192.
Step-by-step explanation:
We have , a right rectangular prism has edge lengths of 2 inches, 3 inches, and 32 inches. We need to find , how many cubes with edge lengths of 1 inch would be needed to fill the prism. Now, in order to find this we need to divide volume of rectangular prism from volume of cubes i.e.
Volume of rectangular prism :
⇒ [tex]v_{1} = length(breadth)(width)\\ v_{1} = 2(3)(32)\\v_{1} = 192in^{3}[/tex]
Volume of cube :
⇒ [tex]v_{2} = length^{3}\\ v_{2} =1^{3}\\v_{2} = 1in^{3}[/tex]
Number of cubes needed = [tex]\frac{v_1}{v_2}[/tex]
⇒ Number of cubes needed = [tex]\frac{v_1}{v_2}[/tex]
⇒ Number of cubes needed = [tex]\frac{192in^{3}}{1in^{3}}[/tex]
⇒ Number of cubes needed = [tex]192[/tex]
∴ Volume of rectangular prism is [tex]192in^{3}[/tex] & Volume of cube is [tex]1in^{3}[/tex] and , cubes with edge lengths of 1 inch would be needed to fill the prism is 192.
