Lewis has a copper pipe with a length of 150 cm and a mass of 800 grams. He cuts a piece of the copper pipe with a length of 90 cm. How do you work out the mass of this piece of copper pipe?

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Answer 1 · 2017-06-09T01:08:46

I got $477 g$ $477g$

I would consider the Linear Density of the pipe as:

$δ = Linear Density = \frac{mass}{length}$ $delta="Linear Density"="mass"/"length"$

or:

$δ = \frac{800}{150} = 5.3 \frac{g}{c m}$ $delta=800/150=5.3g/(cm)$

When you cut it you are left with $90 c m$ $90cm$ of pipe but with the same linear density $δ$ $delta$ so we can write:

$5.3 = \frac{m}{90}$ $5.3=m/90$

or

$m = 5.3 \cdot 90 = 477 g$ $m=5.3*90=477g$

Answer 2 · 2017-06-09T02:07:15

The $90 cm$ $"90 cm"$ piece of the pipe will have a mass of $480 g$ $"480 g"$ .

From the question, we get a relationship of equality between the length and mass of the pipe.

$150 cm = 800 g$ $"150 cm = 800 g"$

There are two conversion factors as shown below.

$\frac{150 cm}{800 g}$ $"150 cm"/"800 g"$ or $\frac{800 g}{150 cm}$ $"800 g"/"150 cm"$

Multiply $90 cm$ $"90 cm"$ by the conversion factor that cancels cm.

$90color(red)cancel(color(black)("cm"))xx(800"g")/(150color(red)cancel(color(black)("cm")))="480 g"$