Year 10 Interactive Maths - Second Edition

Variation as the Square, Cube or Square Root

So, the volume of a sphere varies directly as the cube of its radius.

Example 12

The distance, d m, through which a cricket ball falls after reaching its maximum altitude varies as the square of the elapsed time, t s. The ball takes 3 seconds to fall 44.1 m. How long will it take to fall through 78.4 m?

Solution:

Substituting for k in (1) gives:

This is the formula which relates d and t.

So, the time taken to fall through 78.4 m is 4 seconds.