Question

A mining company uses a rectangular pond of 1,296 m3 to deposit waste chemicals from the extraction processes. In this pond the depth is twice the width and the length is three times the width. What is the depth of the pond? Remember that the volume of a rectangle is length by width and height.

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Answer to a math question A mining company uses a rectangular pond of 1,296 m3 to deposit waste chemicals from the extraction processes. In this pond the depth is twice the width and the length is three times the width. What is the depth of the pond? Remember that the volume of a rectangle is length by width and height.

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Adonis
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102 Answers
1. Denotar las dimensiones del estanque rectangular:
- Largo: 3x
- Ancho: x
- Profundidad: 2x

2. Utilizar la fórmula del volumen para expresar el volumen del estanque en función de x:
V = (3x) \cdot x \cdot (2x)

3. Igualar al volumen dado de 1296 m³ y resolver para x:

3x \cdot x \cdot 2x = 1296

6x^3 = 1296

4. Dividir ambos lados por 6:

x^3 = \frac{1296}{6}

x^3 = 216

5. Tomar la raíz cúbica de ambos lados:

x = \sqrt[3]{216}

x = 6

6. Multiplicar x por 2 para encontrar la profundidad:

2x = 2 \cdot 6

7. Respuesta:

2x = 12\, \text{m}

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