Answer:
The volume of the second rectangular prism is 576 cm³ .
Step-by-step explanation:
As given
The volume of a rectangular prism varies jointly with the length and width when the height remains constant.
Let us assume that the length is denoted by L .
Let us assume that the Breadth is denoted by B.
Thus
[tex]V \propto L\times B[/tex]
V = L × B × H
where H is the constant of variation
The volume of a rectangular prism is 672 cubic centimeters and has a length of 8 centimeters and a width of 14 centimeters.
Volume (V) = 672 cm
Length (L) = 8 cm
Width (B) = 14 cm
Put all the values in the above
672 = 8 × 14 × H
672 = 112H
[tex]H = \frac{672}{112}[/tex]
H = 6
As given
A second prism has a length of 12 centimeters and a width of 8 centimeters.
Length = 12 cm
Width = 8 cm
Height = 6cm
Put all the values in V = L × B × H .
V = 12 × 8 × 6
V = 576 cm³
Therefore the volume of the second rectangular prism is 576 cm³ .
