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    Question

    A triangular field has sides 13 m, 14 m, and 15 m. A

    well with a diameter of 7 m is dug outside the field. If the entire soil dug from the well is used to level the field, find the depth of the well.
    A 1.09 m Correct Answer Incorrect Answer
    B 1.4 m Correct Answer Incorrect Answer
    C 1.5 m Correct Answer Incorrect Answer
    D 1.6 m Correct Answer Incorrect Answer

    Solution

    Area of triangle using Heron’s formula: s = (13 + 14 + 15) / 2 = 21 Area = √[21(21 - 13)(21 - 14)(21 - 15)] = √[21 × 8 × 7 × 6] = √7056 = 84 m² Volume of soil dug = Area of field × depth Volume of well = πr²h = (22/7) × (7/2)² × h = 77h 84 = 77h h = 84/77 = 1.09 m Correct option: a

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