Perimeters, Areas and Volumes


Start off by referring to Key Skills - Formulas

and

Key Skills - Measurement

Hectares

A hectare is an area of 10,000m2

If it was as square it would have sides of 100m.

The previous statement is consistent with the idae that the area of a square or rectangle is just one side multiplied by the other. This is straight forward enough, but be absolutely certain that all sides to be multiplied are in the same units.

This calculation of area generalizes to cubes or cuboids, e.g. the volume of a cardboard box containing a TV set is just the lengths of the three sides multiplied together just so long as all the lengths are given in the same units, e.g. all in centimeters or all in meters.

At GCSE level, this definition of volume generalizes into finding the volumes of compliocated shapes which nevertheless have constant cross-sections.

Going back to the square hectare, let's consider how many will fit into a square kilometer. Along one side of the square kilometer, ten hectares will fit exactly - and likewise for the other side of the square kilometer. Therefore 100 hectares will fit into a square kilometer, using the same logic that tells you there are 64 squares on a chess board because there are 8 squares along one side and eight squares along the other, giving a total number of squares of 8 x 8 = 64.

"Packing"


How many light bulbs can fit completely into the larger carton?

Pack the light bulb boxes in the same orientation shown in the diagram

Along a side of 40cm, five bulb boxes can be packed completely

Along a side of 60cm, six bulb boxes can be packed completely.

So total number of bulb boxes that can be packed is

5 x 5 x 6 = 150