Problem

A spherical ball of ice of radius $12$ cm is placed in a bucket of water.

In a model of the situation,

• the ball remains spherical as it melts
• $t$ minutes after the ball of ice is placed in the bucket, its radius is $r$ cm
• the rate of decrease of the radius of the ball of ice is inversely proportional to the square of the radius
• the radius of the ball of ice is $6$ cm after $15$ minutes

Using the model and the information given,

(a) find an equation linking $r$ and $t$,

(b) find the time taken for the ball of ice to melt completely.

(c) On Diagram 1 on page 27, sketch a graph of $r$ against $t$.