Answer:
The volume increased eightfold.
Step-by-step explanation:
The formula of a volume of a rectangular prism:
[tex]V=lwh[/tex]
l - length
w - width
h - height
We have l = 5cm, w = 7cm and h = 12cm.
Substitute:
[tex]V=(5)(7)(12)=420\ cm^3[/tex]
Doubled the dimensions:
l' = (2)(5cm) = 10cm, w' = (2)(7cm) = 14cm, h = (2)(12cm) = 24cm.
Calculate the new volume:
[tex]V'=(10)(14)(24)=3360cm^3[/tex]
Calculate the quotient [tex]\dfrac{V'}{V}[/tex]
[tex]\dfrac{3360}{420}=8[/tex]
Generalization:
V = lwh - the volume of a prism l × w × h
2l × 2w × 2h - new dimensions
V' = (2l)(2w)(2h) = 8lwh = 8V - new volume
