Answer:
volume becomes 8 times of original rectangular prism
Step-by-step explanation:
Given dimension of prism : 5 cm by 7 cm and a height of 12 cm
volume of prism is given by = length * width * height
thus volume of given prism = 5*7* 12 cubic cm = 420 cubic units.
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next given that all the dimensions are double
the new dimension are
width = 5*2 cm = 10 cm
length = 7*2 cm = 14 cm
height = 12*2 cm = 24 cm
Volume of new prism = 10*14*24 cubic cm = 3,360 cubic units.
3,360 = 8*420 (420 is volume of original cube)
Thus , volume becomes 8 times of old rectangular prism.
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it can be solved even if we do not have any dimension.
if x,y ,z care dimension of rectangular prism
then its volume = x*y*z cubic units
now if dimension are doubled then new dimensions are
2x,2y,2z
thus,
new volume = 2x*2y*2z cubic units = 8xyz cubic units
Thus , we see volume is 8 times of original cube.
