1. **Problem 1: Solve for $t$ in the equation** $$10c = \frac{1}{4} (16p - 8t)$$ 2. **Start by eliminating the fraction by multiplying both sides by 4:** $$4 \times 10c = 4 \times \frac{1}{4} (16p - 8t)$$ $$40c = 16p - 8t$$ 3. **Isolate the term with $t$ by subtracting $16p$ from both sides:** $$40c - 16p = -8t$$ 4. **Divide both sides by $-8$ to solve for $t$:** $$t = \frac{40c - 16p}{-8}$$ 5. **Simplify the fraction by factoring numerator and denominator:** $$t = \frac{\cancel{8}(5c - 2p)}{-\cancel{8}} = -(5c - 2p)$$ 6. **Distribute the negative sign:** $$t = -5c + 2p$$ --- 7. **Problem 2: Solve for $h$ in the volume formula** $$V = \frac{1}{3} \pi r^2 h$$ 8. **Multiply both sides by 3 to eliminate the fraction:** $$3V = 3 \times \frac{1}{3} \pi r^2 h$$ $$3V = \pi r^2 h$$ 9. **Divide both sides by $\pi r^2$ to isolate $h$:** $$h = \frac{3V}{\pi r^2}$$ **Final answers:** - For $t$: $$t = -5c + 2p$$ - For $h$: $$h = \frac{3V}{\pi r^2}$$