SATHEE: Quantitative Aptitude Ques 1436

Quantitative Aptitude Ques 1436

Question: In the given figure ABCD is a rectangle in which length is twice of breadth. H and G divide the line CD into three equal parts. Similarly points E and F trisect the line AB. A circle PQRS is circumscribed by a square PQRS which passes through the points E, F, G and H. What is the ratio of areas of circle to that of rectangle?

Options:

A) $ 3\pi :7 $

B) $ 3:4 $

C) $ 25\pi :72 $

D) $ 32\pi :115 $

Show Answer

Answer:

Correct Answer: C

Solution:

Let $ AD=3a $ and $ DC=6a $

$ \therefore $ $ DH=HG=GC=\frac{6a}{3}=2a $ $ HM=MG=\frac{2a}{2}=a=SM $ $ NQ=a $ (also) and $ SQ=SM+MN+NQ $ $ =a+3a+a=5a $ Since, diagonal of square, $ SQ=5a $ Diameter of circle, SQ = Diagonal of square, SQ Radius of the circle $ =\frac{5a}{2} $ Area of the circle $ =\pi \times {{( \frac{5a}{2} )}^{2}} $

$ \therefore $ $ \frac{Areaofcircle}{Areaofrectangle}=\frac{25/4(a^{2}\pi )}{3a\times 6a}=\frac{25\pi }{72} $

Quantitative Aptitude Ques 1435

Quantitative Aptitude Ques 1437

Quantitative Aptitude Ques 1436

Options:

Answer:

Solution:

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