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A hangar measuring 76.0 m long and 97.5 m wide has a volume of 964 m³ of concrete. Calculate the thickness of the floor to the nearest cm. Also, convert the height of the tail fin of the aircraft to m

Mathematics

ScanSolve AI Answer

Answer

21000 mm\text{21000 mm}

7410 m2\text{7410 m}^2

13 cm\text{13 cm}

Step-by-step solution

7 steps

2.1.1) Convert the height of the tail fin of the aircraft to millimetres.

  1. Identify the height of the tail fin.

    From the text, the height of the tail fin of the aircraft is 21 m21 \text{ m}.

  2. Convert metres to millimetres.

    There are 1000 mm1000 \text{ mm} in 1 m1 \text{ m}.

    Height in mm=21 m×1000mmm\text{Height in mm} = 21 \text{ m} \times 1000 \frac{\text{mm}}{\text{m}} Height in mm=21000 mm\text{Height in mm} = 21000 \text{ mm}

    The height of the tail fin is 21000 mm\boxed{\text{21000 mm}}.

    2.1.2) Calculate the area of the floor of one bay of the hangar.

  3. Identify the length and width of one bay from Figure 1.

    The length of one bay is 76.0 m76.0 \text{ m}.
    The width (or depth) of the hangar floor is 97.5 m97.5 \text{ m}.

  4. Use the formula for the area of a rectangle.

    Area=length×width\text{Area} = \text{length} \times \text{width} Area=76.0 m×97.5 m\text{Area} = 76.0 \text{ m} \times 97.5 \text{ m} Area=7410 m2\text{Area} = 7410 \text{ m}^2

    The area of the floor of one bay of the hangar is 7410 m2\boxed{\text{7410 m}^2}.

    2.1.3) Calculate the thickness of the floor to the nearest centimetre.

  5. Identify the given volume and the area calculated in 2.1.2.

    The volume of concrete for one bay is 964 m3964 \text{ m}^3.
    The area of the floor of one bay is 7410 m27410 \text{ m}^2.

  6. Use the formula for volume to find the thickness (height).

    Volume=length×width×height\text{Volume} = \text{length} \times \text{width} \times \text{height} Volume=Area×thickness\text{Volume} = \text{Area} \times \text{thickness}

    Rearrange to solve for thickness:

    thickness=VolumeArea\text{thickness} = \frac{\text{Volume}}{\text{Area}} thickness=964 m37410 m2\text{thickness} = \frac{964 \text{ m}^3}{7410 \text{ m}^2} thickness≈0.1299595 m\text{thickness} \approx 0.1299595 \text{ m}
  7. Convert the thickness from metres to centimetres and round to the nearest centimetre.

    There are 100 cm100 \text{ cm} in 1 m1 \text{ m}.

    thickness in cm=0.1299595 m×100cmm\text{thickness in cm} = 0.1299595 \text{ m} \times 100 \frac{\text{cm}}{\text{m}} thickness in cm≈12.99595 cm\text{thickness in cm} \approx 12.99595 \text{ cm}

    Rounding to the nearest centimetre:

    thickness≈13 cm\text{thickness} \approx 13 \text{ cm}

    The thickness of the floor to the nearest centimetre is 13 cm\boxed{\text{13 cm}}.

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