Question

A block of stone has a mass of T tonnes. The density of the stone is 2.5g/cm`^3`. Show that the volume of the block is 0.4T`m^3`?

1 tonne = 1000kg

Answer 1

Here's one way to do it.

Explanation:

Step 1. Convert grams to tonnes

`1 color(red)(cancel(color(black)("g"))) × (1 color(red)(cancel(color(black)("kg"))))/(1000 color(red)(cancel(color(black)("g")))) × ("1 t")/(1000 color(red)(cancel(color(black)("kg")))) = 1 × 10^"-6"color(white)(l) "t"`

Step 2. Convert cubic centimetres to cubic metres

`1 color(red)(cancel(color(black)("cm")))^3 × (("1 m")/(100 color(red)(cancel(color(black)("cm")))))^3 = 1 × 10^"-6"color(white)(l) "m"^3`

Step 3, Calculate the density in the new units

`D = (2.5 color(red)(cancel(color(black)("g"))))/(1 color(red)(cancel(color(black)("cm"^3)))) × (1 × color(red)(cancel(color(black)(10^"-6"))) "t")/(1 color(red)(cancel(color(black)("g")))) × (1 color(red)(cancel(color(black)("cm"^3))))/(1 × color(red)(cancel(color(black)(10^"-6"))) "m"^3) = "2.5 t/m"^3`

Step 4. Calculate the volume

`V = T color(red)(cancel(color(black)("t"))) × ("1 m"^3)/(2.5 color(red)(cancel(color(black)("t")))) = 0.40Tcolor(white)(l) "m"^3`