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Calculate the volume of the silo in m³.

Mathematics

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3.2.1

  1. Convert the height of the silo from centimeters to meters.

    Height(h)=3500 cm=3500100 m=35 m\text{Height} (h) = 3500 \text{ cm} = \frac{3500}{100} \text{ m} = 35 \text{ m}
  2. Calculate the volume of the square silo.

    Side length(s)=17.5 m\text{Side length} (s) = 17.5 \text{ m} Volume of square silo=s×s×h\text{Volume of square silo} = s \times s \times h Volume of square silo=17.5 m×17.5 m×35 m\text{Volume of square silo} = 17.5 \text{ m} \times 17.5 \text{ m} \times 35 \text{ m} Volume of square silo=10718.75 m3\text{Volume of square silo} = 10718.75 \text{ m}^{3}
  3. Calculate the radius of one cylindrical silo.

    Diameter(D)=17.5 m\text{Diameter} (D) = 17.5 \text{ m} Radius(r)=D2=17.5 m2=8.75 m\text{Radius} (r) = \frac{D}{2} = \frac{17.5 \text{ m}}{2} = 8.75 \text{ m}
  4. Calculate the volume of one cylindrical silo using π=3.142\pi = 3.142.

    Volume of cylindrical silo=π×r2×h\text{Volume of cylindrical silo} = \pi \times r^{2} \times h Volume of cylindrical silo=3.142×(8.75 m)2×35 m\text{Volume of cylindrical silo} = 3.142 \times (8.75 \text{ m})^{2} \times 35 \text{ m} Volume of cylindrical silo=3.142×76.5625 m2×35 m\text{Volume of cylindrical silo} = 3.142 \times 76.5625 \text{ m}^{2} \times 35 \text{ m} Volume of cylindrical silo=8419.065625 m3\text{Volume of cylindrical silo} = 8419.065625 \text{ m}^{3}
  5. Calculate the total volume of the silo structure (one square silo and four cylindrical silos).

    Total Volume=Volume of square silo+4×Volume of cylindrical silo\text{Total Volume} = \text{Volume of square silo} + 4 \times \text{Volume of cylindrical silo} Total Volume=10718.75 m3+4×8419.065625 m3\text{Total Volume} = 10718.75 \text{ m}^{3} + 4 \times 8419.065625 \text{ m}^{3} Total Volume=10718.75 m3+33676.2625 m3\text{Total Volume} = 10718.75 \text{ m}^{3} + 33676.2625 \text{ m}^{3} Total Volume=44395.0125 m3\text{Total Volume} = 44395.0125 \text{ m}^{3}

    The volume of the silo is 44395.0125 m3\boxed{44395.0125 \text{ m}^{3}}.

    3.2.2

  6. Identify the radius and height for one cylindrical silo.

    Radius(r)=8.75 m\text{Radius} (r) = 8.75 \text{ m} Height(h)=35 m\text{Height} (h) = 35 \text{ m} π=3.142\pi = 3.142
  7. Substitute the values into the given surface area formula for one cylindrical silo.

    Surface Area=2×π×r2+2×π×r×h\text{Surface Area} = 2 \times \pi \times r^{2} + 2 \times \pi \times r \times h Surface Area=2×3.142×(8.75 m)2+2×3.142×8.75 m×35 m\text{Surface Area} = 2 \times 3.142 \times (8.75 \text{ m})^{2} + 2 \times 3.142 \times 8.75 \text{ m} \times 35 \text{ m}
  8. Calculate the surface area.

    Surface Area=2×3.142×76.5625 m2+2×3.142×306.25 m2\text{Surface Area} = 2 \times 3.142 \times 76.5625 \text{ m}^{2} + 2 \times 3.142 \times 306.25 \text{ m}^{2} Surface Area=481.0625 m2+1924.25 m2\text{Surface Area} = 481.0625 \text{ m}^{2} + 1924.25 \text{ m}^{2} Surface Area=2405.3125 m2\text{Surface Area} = 2405.3125 \text{ m}^{2}

    The surface area of one cylindrical silo is 2405.3125 m2\boxed{2405.3125 \text{ m}^{2}}.

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