Multiple choice

Length of the floor of a rectangular auditorium is $6$m more than the radius of a circle with a circumference of $572$m. The perimeter of the floor of the rectangular auditorium is $356$m. What will be the cost of flooring the auditorium(only the floor of the auditorium), if the cost of flooring is Rs. $12/m^2?$

  1. Rs. $87,954$
  2. Rs. $91,236$
  3. Rs. $94,284$
  4. Rs. $75,490$

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Circumference = 2 * pi * r = 572, so r = 572 / (2 * 22/7) = 91m. Length = 91 + 6 = 97m. Perimeter = 2(L + B) = 356, so 97 + B = 178, B = 81m. Area = 97 * 81 = 7857 m^2. Cost = 7857 * 12 = 94284.

AI explanation

Using the circumference formula 2 times pi times radius equals 572, the radius is 91 meters. The length of the auditorium is 6 meters more than this radius, equalling 97 meters. With a perimeter of 2 times length plus 2 times width equaling 356 meters, the width is 81 meters, making the floor area 97 times 81, which is 7857 square meters. Multiplying this area by 12 rupees per square meter gives a total cost of 94284 rupees.

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