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A cylindrical culvert has an internal diameter of 1.05 m. What is its internal surface area?

Mathematics

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Answer

1.05πL m2\text{}1.05 \pi L \text{ m}^2\text{}

Step-by-step solution

4 steps
  1. Identify the given information.

    The internal diameter of the cylindrical culvert is d=1.05d = 1.05 m.

  2. State the formula for the internal surface area of a cylinder.

    The internal surface area of a cylindrical culvert refers to its lateral surface area. The formula for the lateral surface area (AA) of a cylinder is:

    A=πdLA = \pi d L

    where dd is the diameter and LL is the length of the culvert.

  3. Identify missing information.

    The length (LL) of the culvert is not provided in the question. Without this value, the numerical internal surface area cannot be calculated.

  4. Express the internal surface area in terms of the given diameter and the unknown length.

    Substituting the given diameter into the formula:

    A=π(1.05 m)LA = \pi (1.05 \text{ m}) L A=1.05πL m2A = 1.05 \pi L \text{ m}^2

    The internal surface area of the culvert is 1.05πL m2\boxed{\text{}1.05 \pi L \text{ m}^2\text{}}, where LL is the length of the culvert.

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