SOLUTION: The length and width of a rectangular solid are decreased by 30%, and the height is doubled. The ratio of the volume of the new solid to the volume of the original solid is __

Algebra ->  Volume -> SOLUTION: The length and width of a rectangular solid are decreased by 30%, and the height is doubled. The ratio of the volume of the new solid to the volume of the original solid is __      Log On


   

Question 1199716: The length and width of a rectangular solid are decreased by 30%, and the height is doubled. The ratio of the volume of the new solid to the volume of the original solid is __
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
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It is   0.7*0.7*2 = 0.98.         ANSWER


Solved.


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A post-solution note :   the standard name for this solid is  " a rectangular prism ".

Use it for smooth reading.



Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

L = length
W = width
H = height
volume = LWH

The length and width are decreased by 30%
They keep the remaining 70%
0.7L and 0.7W represent the new length and width respectively.
The height is doubled to go from H to 2H

new volume = (new length)*(new width)*(new height)
new volume = (0.7L)*(0.7W)*(2H)
new volume = (0.7*0.7*2)*(LWH)
new volume = (0.7*0.7*2)*(old volume)
new volume = 0.98*(old volume)
(new volume)/(old volume) = 0.98

Interpretation:
The new volume is 98% of the old volume
In other words, there is a 2% loss in volume.
It would be like going from 100 cubic inches to 98 cubic inches.