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CBSE - X - Mathematics - Surface Areas and Volumes

What is the ratio of the area of the circle to the area of an equilateral triangle, if the diameter of the circle is equal to the side of the triangle.

Asked by anujha.anujha 25th February 2015, 7:22 PM
Answered by Expert

Answer:

A r e a space o f space c i r c l e space equals space straight pi cross times left parenthesis radius right parenthesis squared space equals space straight pi space cross times space open parentheses diameter over 2 close parentheses squared space equals space fraction numerator straight pi cross times straight d squared over denominator 4 end fraction Area space of space equilateral space triangle space equals space fraction numerator square root of 3 over denominator 4 end fraction cross times space left parenthesis side right parenthesis squared  fraction numerator straight A straight r straight e straight a space straight o straight f space straight c straight i straight r straight c le over denominator Area space of space equilateral space triangle end fraction space equals space fraction numerator fraction numerator straight pi cross times straight d squared over denominator 4 end fraction over denominator fraction numerator square root of 3 over denominator 4 end fraction cross times space left parenthesis side right parenthesis squared end fraction But space diameter space equals space side space of space the space triangle comma  fraction numerator straight A straight r straight e straight a space straight o straight f space straight c straight i straight r straight c le over denominator Area space of space equilateral space triangle end fraction space equals space fraction numerator fraction numerator straight pi cross times straight d squared over denominator 4 end fraction over denominator fraction numerator square root of 3 over denominator 4 end fraction cross times straight d squared end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space fraction numerator straight pi over denominator square root of 3 end fraction
Answered by Expert 26th February 2015, 3:47 PM

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