Subjects geometry

Pond Volume 21A93A

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1. **Problem statement:** A fish pond is a rectangular prism with length 4 m, width 3 m, and depth 2 m. 2. **Find the volume of the empty pond:** The volume $V$ of a rectangular prism is given by the formula: $$V = \text{length} \times \text{width} \times \text{height}$$ 3. **Calculate the volume:** $$V = 4 \times 3 \times 2 = 24 \text{ cubic meters}$$ 4. **Find the volume of water when filled to 1.5 m depth:** Height for water volume calculation is $1.5$ m. 5. **Convert dimensions to centimetres:** Length: $4 \text{ m} = 400 \text{ cm}$ Width: $3 \text{ m} = 300 \text{ cm}$ Height: $1.5 \text{ m} = 150 \text{ cm}$ 6. **Calculate volume in cubic centimetres:** $$V = 400 \times 300 \times 150 = 18,000,000 \text{ cm}^3$$ 7. **Convert volume to litres:** Since $1000 \text{ cm}^3 = 1 \text{ L}$, $$\frac{18,000,000}{1000} = 18,000 \text{ L}$$ **Final answers:** - Volume of empty pond: $24$ cubic meters - Height for water volume: $1.5$ m - Length in cm: $400$ cm - Width in cm: $300$ cm - Height in cm: $150$ cm - Volume of water: $18,000,000$ cm$^3$ - Volume in litres: $18,000$ L