CAT 2020 Question Paper | Quants Slot 1

CAT Previous Year Paper | CAT Quants Questions | Question 22

This question is from Mensuration. Mensuration is a very intuitive topic. You can expect at least one question from this topic in the CAT exam. The questions from Mensuration can be solved with a practical approach even if one is not completely prepared for the entire Geometry section in CAT. This question hovers around a circle that is inscribed in a triangle. Then the Circle is painted. We need to find the perimeter of the rectangle. Make sure you master Mensuration by practising CAT Previous Year Question paper. From now on, you should not be able to look at a bucket without thinking of it as a cone carved out from another cone!

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 the sheet left unpainted is two-thirds of the painted area then 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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