1. **Problem statement:** Calculate the volume of wood used for two wooden tubs (trækær 1 and trækær 2) and their capacities in liters. 2. **Given data:** - Trækær 1 dimensions (cm): 210 × 65 × 80 (rectangular prism) - Trækær 2 dimensions (cm): depth 210, front is a trapezoid with bases 102 cm and 80 cm, height 64 cm 3. **Formulas:** - Volume of rectangular prism: $$V = l \times w \times h$$ - Volume of trapezoidal prism: $$V = \text{area of trapezoid} \times \text{depth}$$ - Area of trapezoid: $$A = \frac{(a+b)}{2} \times h$$ where $a$ and $b$ are the bases and $h$ is the height - Convert cubic centimeters to cubic meters: $$1\,m^3 = 1,000,000\,cm^3$$ - Convert cubic centimeters to liters: $$1\,L = 1000\,cm^3$$ 4. **Calculate volume of trækær 1:** $$V_1 = 210 \times 65 \times 80 = 1,092,000\,cm^3$$ Convert to cubic meters: $$V_1 = \frac{1,092,000}{1,000,000} = 1.092\,m^3$$ 5. **Calculate volume of trækær 2:** Area of trapezoid front: $$A = \frac{(102 + 80)}{2} \times 64 = \frac{182}{2} \times 64 = 91 \times 64 = 5824\,cm^2$$ Volume: $$V_2 = 5824 \times 210 = 1,222,944\,cm^3$$ Convert to cubic meters: $$V_2 = \frac{1,222,944}{1,000,000} = 1.222944\,m^3$$ 6. **Calculate capacity in liters:** - Trækær 1: $$\text{Capacity}_1 = \frac{1,092,000}{1000} = 1092\,L$$ - Trækær 2: $$\text{Capacity}_2 = \frac{1,222,944}{1000} = 1222.944\,L$$ **Final answers:** - Volume of wood used for trækær 1: $1.092\,m^3$ - Volume of wood used for trækær 2: $1.222944\,m^3$ - Capacity of trækær 1: $1092\,L$ - Capacity of trækær 2: $1222.944\,L$