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Calculate the volume of reinforce concrete for the pipe and the volume of water that can fill the pipe in litre.

Mathematics

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2 parts
a

0.0118 m3\text{}0.0118 \, \text{m}^3\text{}

b

38.5 litres\text{}38.5 \, \text{litres}\text{}

Step-by-step solution

4 steps

Voici les calculs pour les volumes demandés :

Part a· 2 steps

Le volume de béton armé pour le tuyau

Le tuyau est un cylindre creux. Le volume de béton armé est la différence entre le volume du cylindre extérieur et le volume du cylindre intérieur.

  1. Convertir les rayons en mètres.

    Le rayon externe R=80 mm=0.08 mR = 80 \, \text{mm} = 0.08 \, \text{m}.
    Le rayon interne r=70 mm=0.07 mr = 70 \, \text{mm} = 0.07 \, \text{m}.
    La longueur du tuyau L=2.5 mL = 2.5 \, \text{m}.

  2. Calculer le volume du béton armé.

    La formule du volume d'un cylindre creux est V=π(R2−r2)LV = \pi (R^2 - r^2) L.

    Vbeˊton=π((0.08 m)2−(0.07 m)2)×2.5 mV_{\text{béton}} = \pi ((0.08 \, \text{m})^2 - (0.07 \, \text{m})^2) \times 2.5 \, \text{m} Vbeˊton=π(0.0064 m2−0.0049 m2)×2.5 mV_{\text{béton}} = \pi (0.0064 \, \text{m}^2 - 0.0049 \, \text{m}^2) \times 2.5 \, \text{m} Vbeˊton=π(0.0015 m2)×2.5 mV_{\text{béton}} = \pi (0.0015 \, \text{m}^2) \times 2.5 \, \text{m} Vbeˊton=0.00375π m3V_{\text{béton}} = 0.00375 \pi \, \text{m}^3 Vbeˊton≈0.01178 m3V_{\text{béton}} \approx 0.01178 \, \text{m}^3

    Le volume de béton armé pour le tuyau est 0.0118 m3\boxed{\text{}0.0118 \, \text{m}^3\text{}}.

Part b

38.5 litres\text{}38.5 \, \text{litres}\text{}

Le volume d'eau qui peut remplir le tuyau en litres

Le volume d'eau qui peut remplir le tuyau est le volume interne du tuyau.

  1. Calculer le volume interne du tuyau en mètres cubes.

    La formule du volume d'un cylindre est V=πr2LV = \pi r^2 L.

    Veau=π(0.07 m)2×2.5 mV_{\text{eau}} = \pi (0.07 \, \text{m})^2 \times 2.5 \, \text{m} Veau=π(0.0049 m2)×2.5 mV_{\text{eau}} = \pi (0.0049 \, \text{m}^2) \times 2.5 \, \text{m} Veau=0.01225π m3V_{\text{eau}} = 0.01225 \pi \, \text{m}^3 Veau≈0.03845 m3V_{\text{eau}} \approx 0.03845 \, \text{m}^3

  2. Convertir le volume de mètres cubes en litres.

    On sait que 1 m3=1000 litres1 \, \text{m}^3 = 1000 \, \text{litres}.

    Veau, litres=0.03845 m3×1000 litres/m3V_{\text{eau, litres}} = 0.03845 \, \text{m}^3 \times 1000 \, \text{litres/m}^3 Veau, litres≈38.45 litresV_{\text{eau, litres}} \approx 38.45 \, \text{litres}

    Le volume d'eau qui peut remplir le tuyau est 38.5 litres\boxed{\text{}38.5 \, \text{litres}\text{}}.

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