Suppose the dimensions of a rectangular prism are enlarged by a factor of 3. By what scale factor will the volume of the prism be scaled ?
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since volume is cubic you need to take the cube of the length multiplier
here is a simple task....
image a cube with a side length of 1 unit... find the volume
then double the side length of the cube... what is the volume..?
the linear scaling factor is 1: 2
what is the ratio of the volumes.. 1:?
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Wouldn't it be 1:2 ?
Well, a rectangular prism has length, width, and height.
Let's plug in some numbers. Say for a rectangular prism, you had 2, 3, and 4 for length, width, and height respectively. The volume would be 24.
I think the question means by "enlarged by a factor of 3" that you multiply each measurement by 3.
So now you'd have 6, 9, and 12 for length, width and height. Multiply those and you'd get a volume 648.
Then you'd find out how many times 24 would go into 648 to get your answer.
Pro tip: you can plug in easy, small numbers for some of these problems to help you get the answer.
Hopefully that made sense :)
That did make sense .. But in the question it didn't give me any other numbers for length width or height or even volume. All it said was it would be enlarged by a factor of 3 .. So that's wat got me confused
no the ratio of the volumes isn't 1:2
the volume of a cube 1 unit is 1 unit^3
volume of a cube 2 units is 8 units ^3
so if the linear ratio is 1:2 the volume ratios are 1:8
which can be written as 1^3:2^3
so a cube with a side length of 3 has a volume 27 units^3
the ratio of the volumes of 2 cubes with linear scaling factor of 2:3
is 8:27 or 2^3:3^3
so if you know the linear scaling factor the cube of the scaling factor will give the ratio of the volumes...
same idea works for area... if the know the linear scaling factor then the ratio of the areas is the square of the scaling factor
hope it makes sense
Oh that made perfect sense .. And I made a mistake at the top cause I forgot it was by cube but thanks so much
@kenialove I can see why you got confused. I don't think the question was worded properly.
When you face a question that doesn't give you values, it's always worth a shot at plugging in your own values. It works on standardized tests and on homework alike, so it's a good strategy to keep in your toolbox :)
Thanks ! @anitasonia98 that would come in handy a lot