Question

A castle is surrounded by a circular moat which is 5 m wide
and 2 m deep. The diameter of the outer edge of the moat is
50 m. Find, in kilolitres, the quantity of water in the moat.

Answers

  1. Answer:
      1414 kL
    Step-by-step explanation:
    The volume of the donut-shaped moat is the product of its surface area and depth. The area is the product of its centerline length and its width.

    Moat area

    The diameter of the centerline of the moat is (50 m -5 m) = 45 m. The length of that centerline is …
      C = πd = π(45 m) = 45π m
    The area is this length times the width of the moat:
      moat area = (45π m)(5 m) = 225π m²

    Moat volume

    The volume is the product of the area and the depth of the moat:
      V = Ah = (225π m²)(2 m) = 450π m³ ≈ 1413.72 m³
    1 cubic meter is 1000 liters, 1 kiloliter.
    The volume of the moat is about 1414 kL.

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