1. **State the problem:** We are given the formula for the Ponderal Index: $$P = \frac{M}{h^3}$$ where $P$ is the Ponderal Index, $M$ is the mass (weight), and $h$ is the height. 2. **Rearrange the formula to find height $h$ in terms of $P$ and $M$:** Starting with $$P = \frac{M}{h^3}$$ Multiply both sides by $h^3$: $$Ph^3 = M$$ Divide both sides by $P$: $$h^3 = \frac{M}{P}$$ Take the cube root of both sides to solve for $h$: $$h = \sqrt[3]{\frac{M}{P}}$$ 3. **Calculate Mary's height given $P = 13$ and $M = 67.5$ kg:** Substitute values into the formula: $$h = \sqrt[3]{\frac{67.5}{13}}$$ Calculate the fraction: $$\frac{67.5}{13} \approx 5.1923$$ Now find the cube root: $$h \approx \sqrt[3]{5.1923} \approx 1.74$$ 4. **Final answer:** Mary's height is approximately **1.74 metres** (to 2 decimal places).