1. **Find the missing length $x$ in the right triangular prism with volume 432 cm³.** The volume formula for a triangular prism is: $$V = \text{Area of triangular base} \times \text{height}$$ The triangular base area is: $$A = \frac{1}{2} \times 12 \times 8 = 48 \text{ cm}^2$$ Given volume $V = 432$ cm³, height $h = x$ cm, so: $$432 = 48 \times x$$ Solve for $x$: $$x = \frac{432}{48}$$ Intermediate step with cancellation: $$x = \frac{\cancel{432}}{\cancel{48}} = 9$$ So, $x = 9$ cm. 2. **Find the missing length $x$ in the rectangular prism with volume 420 cm³.** Volume formula for rectangular prism: $$V = \text{length} \times \text{width} \times \text{height}$$ Given $V = 420$ cm³, height = 5 cm, depth = 8 cm, width = $x$ cm: $$420 = 5 \times 8 \times x$$ Simplify: $$420 = 40x$$ Solve for $x$: $$x = \frac{420}{40}$$ Intermediate step with cancellation: $$x = \frac{\cancel{420}}{\cancel{40}} = 10.5$$ So, $x = 10.5$ cm. 3. **Calculate the volume of water in a cylindrical tank filled to 80% of its height.** Given radius $r = 2$ m, height $h = 5$ m, filled height $= 0.8 \times 5 = 4$ m. Volume of cylinder: $$V = \pi r^2 h$$ Calculate volume of water: $$V = \pi \times 2^2 \times 4 = 16\pi$$ Approximate: $$V \approx 16 \times 3.1416 = 50.27$$ So, volume of water is approximately 50.27 cubic meters. 4. **Calculate total volume of cake batter for 5 cylindrical cakes.** Given radius $r = 10$ cm, height $h = 15$ cm. Volume of one cake: $$V = \pi r^2 h = \pi \times 10^2 \times 15 = 1500\pi$$ Total volume for 5 cakes: $$5 \times 1500\pi = 7500\pi$$ Approximate: $$7500 \times 3.1416 = 23562$$ So, total volume is approximately 23562 cubic centimeters.