The cost of a circular badge is directly proportional to the square of its radius. The cost of a badge with radius of $2\text{ cm}$ is $\text{£}0.68$. Find:

- a formula connecting the cost of the badge and its radius.
- the cost of a badge of radius $2.4 \text{ cm}$
- the radius of a badge costing $\text{£}1.53$