CTET 2 Math and Science Jul 2013 Paper

Question : 42 of 120

Marks: +1, -0

A square and a circle have equal perimeters. The ratio of the area of the square to the area of the circle is

Solution:

According to question,
Perimeter of Square = Circumference of Circle

4a=2πr

(a = side of square, r = radius of circle)

⇒2a=πr

∴a={πr}/2

\text "Ratio of their areas"=\;\;{\;\text"Area of square"\;}/{\;\text"Area of circle"\;}

=\;\;{a^{2}}/{πr^{2}}=\;\;{(\;\;{πr}/{2})^{2}}/{πr^{2}}=\;\;{(πr)^{2}}/{4×πr^{2}}=\;\;{π}/{4}=π:4

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