maths question about volume

Jonnybmac

Jonnybmac

Jonnybmac

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can anyone explain why both values are written with the same cm^3? 10cm^3(cubed) is obviously 10cm * 10cm * 10cm, but why is the answer written as (1000cm^3) surely if i was to look at 1000cm^3, how do i know that its derived from 10cm cubed and not that it's 1000cm * 1000cm * 1000cm?

i know you can write 1cm^3 as 1 ml or 10cm^3 = 1000ml but why is it okay to use cm^3 or am i missing something
 
cm^3 is "cubic centimetres". This is the unit you use to measure 3D things (like volumes). A "centimeter" is a 2D measurement that can only be used for things like length, it has no meaning in 3 dimensions.

10^3cm is not the same as 10cm^3
 
so in getting this right, 10cm^3 is equal to what?

for example:

140cm * 50cm * 30cm = 210000(cm^3)?

what would i use in the brackets

so you're saying it should be 10^3cm = 1000cm^3 ?
 
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sorry i didnt mean to write what you both quoted, i just got a little confused, is this correct? 10^3cm = 1000cm^3

i was under the impresion that to explain a 10cmx10cmx10cm box you would write 10cm^3
 
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Jonnybmac said:
sorry i didnt mean to write what you both quoted, i just got a little confused, is this correct? 10^3cm = 1000cm^3

i was under the impresion that to explain a 10cmx10cmx10cm box you would write 10cm^3
Click to expand...

The area of 10cm x 10cm square would be 100cm^2 (squared).

Similarly, the volume of a 10cm x 10cm x 10cm cube would be 1000cm^3 (cubed).
 
Jonnybmac said:
sorry i didnt mean to write what you both quoted, i just got a little confused, is this correct? 10^3cm = 1000cm^3

i was under the impresion that to explain a 10cmx10cmx10cm box you would write 10cm^3
Click to expand...

No, the unit (cm^3) is a separate thing to the number.
If it helps, let's call it a cc, cubic centimetre.

1cm x 1cm x 1cm is 1cc.
10cm x 10cm x 10cm is 1,000cc
 
To help everyone with the typing:
Hold Alt while pressing 0178 on the numpad gives ²
Hold Alt while pressing 0179 on the numpad gives ³
or you can just copy them from my post.
 
Jonnybmac said:
I think I got it now and thanks for the help. I was trying to put dimentions under a power notation, which i guess is a no no
Click to expand...

Yeah you can. You have to distinguish between the value and the unit is all. If the units are SI they combine. You work out the values and the units separately. Lots of equations are like that, you work out the values but also the units. With the units some may cancel out or have raised powers.

With the volume example 10m x 10m x 10m, it's 10x10x10 and mxmxm, so with notation it's 10³m³
 
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