AD is the diameter of a circle with area 707 m² and AB = BC = CD

Ques.100

AD is the diameter of a circle with area 707 m² and AB = BC = CD as shown in the figure above. All curves inside the circle are semicircles with their diameters on AD. What is the cost of levelling the shaded region at the rate of Rs. 63 per square metre?
(a) Rs. 29, 700
(b) Rs. 22, 400
(c) Rs. 14, 847
(d) None of the above

 

Anurag Mishra Professor Asked on 20th February 2016 in Maths.
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  • 1 Answer(s)
    Best answer

    Answer: (d) None of the above 

    Solution:-
    The area of the circle = 707 m²

    Formula-
    The area of the circle = πr²

    Then,  πr² = 707                                               (π = 22/7)
    22 x r²/7 = 707
    r² = 707 x 7/22
    r² = 224.9545
    Square root on both side,
    r = 14.99 or 15
    r = 15 m

    AB = BC = CD                  (Given in the question)
    Then, AB = 5 m
    Therefore, the radius of the circle = 5/2 = 2.5 m
    So, the area of the circle which diameter AB = 22 x 2.5 x 2.5/2 x 7
    = 9.82 m²
    Thus, the area of both smallest semicircle = 2 x 9.82
    = 19.64 m²

    AC = 10 m
    Therefore, radius of the circle = 10/2 = 5 m
    So, the area of the semicircle = 22 x 5 x 5 /7 x 2
    = 39.28 m²
    Thus, the area of both big semicircles = 2 x 39.28
    = 78.57 m²

    Then, area of the shaded part = 78.57 – 19.64
    = 58.93 m²

    Rate of the leveling = Rs. 63 per square meter
    So, cost of the leveling the shaded region = 58.93 x 63
    = Rs. 3712.68

    Hence, the correct answer is option (4) None of the above.

    Anurag Mishra Professor Answered on 20th February 2016.
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