Volume question. Unit conversation error

[MathsFormula]

Hello, when I first tried this question I got the answer wrong. Then I approached it differently and realised that I was converting the units incorrectly BUT I don't know how to fix my mistake.

The question : A cylindrical container has a capacity of 1.8 litres and a length of 14 cm. Find the diameter.

Method 1

I converted the length 14 cm into metres (because litres is in metres too???). So length = 0.14 m

Volume = length x pi x r²

V = l x pi x r²

1.8 = 0.14 × pi x r²

r = 2

Diameter = 4

WRONG ANSWER


Method 2

I converted the 1.8 litres into centimetres = 1800 cm³

V = l x pi x r²

1800 = 14 x pi x r²

r = 6.39

Diameter = 12.7 cm

Correct answer


Please advise what I did wrong in method ONE.

Thank you

 

[Prove It]

Hello, when I first tried this question I got the answer wrong. Then I approached it differently and realised that I was converting the units incorrectly BUT I don't know how to fix my mistake.

The question : A cylindrical container has a capacity of 1.8 litres and a length of 14 cm. Find the diameter.

Method 1

I converted the length 14 cm into metres (because litres is in metres too???). So length = 0.14 m

Volume = length x pi x r²

V = l x pi x r²

1.8 = 0.14 × pi x r²

r = 2

Diameter = 4

WRONG ANSWER


Method 2

I converted the 1.8 litres into centimetres = 1800 cm³

V = l x pi x r²

1800 = 14 x pi x r²

r = 6.39

Diameter = 12.7 cm

Correct answer


Please advise what I did wrong in method ONE.

Thank you

1 litre is NOT \(\displaystyle \displaystyle \begin{align*} 1\,\textrm{m}^3 \end{align*}\)!

By definition, one millilitre is the amount of liquid that can fit in \(\displaystyle \displaystyle \begin{align*} 1\,\textrm{cm}^3 \end{align*}\), so that means 1L, which is 1000 mL, is the amount of liquid in \(\displaystyle \displaystyle \begin{align*} 1000\,\textrm{cm}^3 \end{align*}\).

But \(\displaystyle \displaystyle \begin{align*} 1\,\textrm{m}^3 = 100^3\,\textrm{cm}^3 = 1\,000\,000\,\textrm{cm}^3 \end{align*}\), NOT \(\displaystyle \displaystyle \begin{align*} 1000\,\textrm{cm}^3 \end{align*}\).

 

[MathsFormula]

But \(\displaystyle \displaystyle \begin{align*} 1\,\textrm{m}^3 = 100^3\,\textrm{cm}^3 = 1\,000\,000\,\textrm{cm}^3 \end{align*}\), NOT \(\displaystyle \displaystyle \begin{align*} 1000\,\textrm{cm}^3 \end{align*}\).

Thanks
Got that bit. 1 litre is 10cm * 10 cm * 10 cm = 1000 cm³

 

[MathsFormula]

Should be:
1.8 = 0.014 * pi * r

Hello, I don't understand why 14 cm is converted to 0.014 m and not 0.14 m

 

[ksdhart2]

Hello, I don't understand why 14 cm is converted to 0.014 m and not 0.14 m

You're absolutely correct that 14cm is 0.14m and not 0.014m. However, that's not the core issue here, but rather it's that you're converting to the wrong units. In your first attempt, you began by (incorrectly) converting all units to meters. Because liter is a volume, you know it will be a cubic unit, so you'll end up with something of the form:

V meters³ = l meters * pi * r meters²

As noted by Prove It, \(\displaystyle 1 \text{L} = 1000 \text{mL} = 1000 \text{cm}^3\) and \(\displaystyle 1 \text{L} \ne 1 \text{m}^3\). Accordingly, \(\displaystyle 1.8 \text{L} = 1.8 \text{dm}^3\), where dm is a decimeter or 1/10th of a meter. So, then your equation is:

1.8 decimeters³ = 0.14 meters * pi * r meters²

Now, can you see why this equation will not give you the correct answer? From that, do you see why the correct value for length is 0.014 when using this method?

 

[Deleted member 4993]

Should be:
1.8 = 0.014 * pi * r

Also, note that it is standard now to use * as multiplication symbol.

Corner .... straight to the corner ....

It should be:

1800 (cc) = π * r² * 14 (cm)

or

1.8 = π * r² * 0.014

\(\displaystyle \displaystyle{r \ = \ \sqrt{\dfrac{1.8}{0.014 * \pi }}}\)