Question

Help with this math question please

Answer 1

There are two main ways of doing this, depending on your level of understanding,and of what you have been taught in class.

First Option

First you could make up lengths that result in a volume of 24dm³, and then halve those lengths and work out the new volume:

For example:

Lets say that:

The height = 4
The width = 3
The length = 2

We know that these result in a volume of 24dm³ (because 4 x 3 x 2 = 24)

Now lets see what happens to the volume when we halve these units

The new height = 2                (because 4 ÷ 2 = 2)
The new width = 1.5               (because 3 ÷ 2 = 1.5)
The length = 1                         (because 2 ÷ 2 = 1)

Now lets work out the new volume:
 2 x 1.5 x 1 = 3dm³
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Answer:
So the new volume will be 3dm³



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Second Option

If you have done the relationship between scale factors of lengths, areas and volumes, then you can work it out another way.

We know the Length Scale Factor is 0.5    ( 1/2)
To get the Volume Scale Factor, we cube ( ³ ) the length scale factor) :

So the Volume Scale Factor is;
     0.5³ = 0.125.

Now that we have the Volume Scale factor, we multiply it by the old volume to get the new volume:

24 x 0.125 = 3dm³

(P.S  if you haven't learnt about this  in class yet, then don't worry about it)
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