1. Problem 3: Find the volume of the bottle crate, a rectangular prism with dimensions 90 cm (length), 60 cm (width), and 80 cm (height). 2. Volume of a rectangular prism is given by the formula: $$\text{Volume} = \text{length} \times \text{width} \times \text{height}$$ 3. Substitute the given values: $$\text{Volume} = 90 \times 60 \times 80$$ 4. Calculate step-by-step: $$90 \times 60 = 5400$$ $$5400 \times 80 = 432000$$ 5. Therefore, the volume of the bottle crate is: $$432000 \text{ cm}^3$$ 6. Problem 4a: Calculate the volume of the pencil case, a triangular prism with triangular base sides 6 cm (base), 8 cm (height), and 10 cm (hypotenuse), and length 32 cm. 7. Volume of a triangular prism is: $$\text{Volume} = \text{area of triangular base} \times \text{length}$$ 8. Area of the triangular base is: $$\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 6 \times 8 = 24$$ 9. Multiply by length: $$24 \times 32 = 768$$ 10. Volume of the pencil case is: $$768 \text{ cm}^3$$ 11. Problem 4b: Calculate the surface area of the pencil case. 12. Surface area of a triangular prism is: $$\text{Surface Area} = \text{perimeter of triangular base} \times \text{length} + 2 \times \text{area of triangular base}$$ 13. Perimeter of triangular base: $$6 + 8 + 10 = 24$$ 14. Calculate lateral surface area: $$24 \times 32 = 768$$ 15. Calculate total surface area: $$768 + 2 \times 24 = 768 + 48 = 816$$ 16. Therefore, the surface area of the pencil case is: $$816 \text{ cm}^2$$