Question

The area of the base of a can of lemonade is 32.4 cm^2, What is this area in mm^2?

Answer 1

`32.4cm^2=3240mm^2`

Explanation:

Note that 1 cm is the same length as 10 mm

Consider a square of side length 1 cm

In cm this area is
`1cmxx1cm=1^2cm^2 = 1cm^2`

In mm the same area is
`10mmxx10mm" "=" "10^2mm^2=100mm^2`

So `" "color(green)(1cm^2=100mm^2)` ............................Equation(1)

But we need 32.4 cm. So we need to change the 1cm in Equation(1) to 32.4

To maintain the correct ratios you have to multiply both sides by the same amount.

`color(green)(color(red)(32.4)xx1cm^2=color(red)(32.4)xx100mm^2)`

`32.4cm^2=3240mm^2`