SOLUTION: A square has twice the perimeter of a circle . the ratio of the area of the square to the area of the circle is
A 4 b pi c 1/pi d 16/pi e none of these
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A 4 b pi c 1/pi d 16/pi e none of these
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Question 280316: A square has twice the perimeter of a circle . the ratio of the area of the square to the area of the circle is
A 4 b pi c 1/pi d 16/pi e none of these
You can put this solution on YOUR website! A square has twice the perimeter of a circle . the ratio of the area of the square to the area of the circle is
A 4 b pi c 1/pi d 16/pi e none of these
Let x be a side of the square. The perimeter of the square is then 4*x. The perimeter (i.e. circumference) of the circle then is (1/2)*4x = 2x. The circumference is also given by pi*diameter = pi*2*r where r is the radius.
So we have pi*2*r = 2*x and
r = 2x/2pi = x/pi
The area of the square is x*x = x^2
The area of the circle with radius r is pi*r^2
The ratios of the two areas is area of square/area of circle.
Using the fact that r = x/pi we the ratios become:
x^2/(pi*(x/pi)^2) =
x^2/(pi*(x^2/pi^2))=
(x^2/x^2)/(pi/pi^2)=
1/pi
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