📢 Too many exams? Don’t know which one suits you best? Book Your Free Expert 👉 call Now!

    Question

    A rhombus has an area of 2,592 cm² and its diagonals are

    in the ratio 5:3. A circle is drawn with the shorter diagonal of the rhombus as its diameter. Calculate the difference between the area of the circle and 75% of the rhombus’s area. (Take π = 3)
    A 480.8 cm² Correct Answer Incorrect Answer
    B 580.4 cm² Correct Answer Incorrect Answer
    C 310.2 cm² Correct Answer Incorrect Answer
    D 391.2 cm² Correct Answer Incorrect Answer

    Solution

    ATQ,

    Let diagonals = 5x and 3x

    (1/2) × 5x × 3x = 7.5x²

    2592 = 7.5x² → x² = 345.6 → x = √345.6 ≈ 18.59

    Smaller diagonal = 3x ≈ 55.77 cm

    Radius ≈ 27.89 cm

    Area of circle ≈ 3 × (27.89)² ≈ 3 × 778.4 ≈ 2335.2 cm²

    75% of rhombus = 0.75 × 2592 = 1944 cm²

    Difference ≈ 2335.2 - 1944 = 391.2 cm²

    Practice Next
    More Circle Questions

    Relevant for Exams:

    ask-question