1. **Problem statement:** Find the volume of a triangular prism with base sides 3 cm, 4 cm, and 5 cm, and height 10 cm. 2. The triangle with sides 3, 4, and 5 is a right triangle (since $3^2 + 4^2 = 5^2$). 3. Calculate the area of the triangular base using the formula for a right triangle: $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 3 \times 4 = 6\text{ cm}^2$$ 4. Volume of the prism is area of base times the prism height: $$\text{Volume} = 6 \times 10 = 60\text{ cm}^3$$ --- 1. **Problem statement:** Find the volume of a regular square pyramid with height 3 m and base perimeter 16 m. 2. Since the pyramid is square-based, each side of the base has length: $$\text{side} = \frac{16}{4} = 4\text{ m}$$ 3. Calculate the area of the square base: $$\text{Area} = 4^2 = 16\text{ m}^2$$ 4. Volume of a pyramid is: $$\text{Volume} = \frac{1}{3} \times \text{base area} \times \text{height} = \frac{1}{3} \times 16 \times 3 = 16\text{ m}^3$$ --- 1. **Problem statement:** Find the liters of water held by an Olympic swimming pool cuboid of dimensions 50 m long, 25 m wide, and 3 m deep. 2. Calculate the volume in cubic meters: $$\text{Volume} = 50 \times 25 \times 3 = 3750\text{ m}^3$$ 3. Convert cubic meters to liters using the conversion factor: $$1\text{ m}^3 = 1000\text{ liters}$$ 4. Therefore: $$\text{Water volume} = 3750 \times 1000 = 3750000\text{ liters}$$