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Question 22 : On a rectangular metal sheet of area 135 sq in, a circle is painted such that the circle touches opposite two sides. If the area of teh sheet left unpainted is two-thirds of teh painted area tehn the perimeter of the rectangle in inches is

  1. 3√π(5 + \\frac{12}{π}))
  2. 4√π(3 + \\frac{12}{π}))
  3. 5√π(3 + \\frac{12}{π}))
  4. 3√π(\\frac{5}{2}) + \\frac{6}{π}))

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Explanatory Answer

Total area = 5 parts
circle area
So, painted area = 135 × \\frac{3}{5}) = π r2
Solving r = \\frac{9}{√π})
Substituting r in l = \\frac{135}{2r})
l = \\frac{15√π}{2})
Perimeter of rectangle = 2(l + b)
= 2(\\frac{15√π}{2}) + \\frac{18}{√π}))
= 3√π (5 + \\frac{12}{π}))

The answer is, "3√π(5 + \\frac{12}{π}))"

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