1. **Stating the problem:** We are given the curved surface area formula of a cone: $$A = \pi r \sqrt{h^2 + r^2}$$ (a) Make $h$ the subject of the formula. (b) Find the height $h$ when $A = 550$ cm$^2$ and $r = 7$ cm, using $\pi = \frac{22}{7}$. 2. **Rearranging the formula to make $h$ the subject:** Start with: $$A = \pi r \sqrt{h^2 + r^2}$$ Divide both sides by $\pi r$: $$\frac{A}{\pi r} = \sqrt{h^2 + r^2}$$ Intermediate step showing cancellation: $$\frac{A}{\cancel{\pi} \cancel{r}} = \sqrt{h^2 + r^2}$$ Square both sides to remove the square root: $$\left(\frac{A}{\pi r}\right)^2 = h^2 + r^2$$ Isolate $h^2$: $$h^2 = \left(\frac{A}{\pi r}\right)^2 - r^2$$ Take the square root of both sides: $$h = \sqrt{\left(\frac{A}{\pi r}\right)^2 - r^2}$$ 3. **Finding the height $h$ for given values:** Given: $$A = 550, \quad r = 7, \quad \pi = \frac{22}{7}$$ Calculate $\pi r$: $$\pi r = \frac{22}{7} \times 7 = 22$$ Calculate $\frac{A}{\pi r}$: $$\frac{550}{22} = 25$$ Substitute into formula for $h$: $$h = \sqrt{25^2 - 7^2} = \sqrt{625 - 49} = \sqrt{576}$$ Calculate the square root: $$h = 24$$ **Final answers:** (a) $$h = \sqrt{\left(\frac{A}{\pi r}\right)^2 - r^2}$$ (b) $$h = 24 \text{ cm}$$