If the perimeter of a circle and a square are equal, then what is the ratio of the area of the circle to that of the square?

Explanation

Given 2\pi r = 4a, so a = \frac{\pi r}{2}. Area of the circle is \pi r^2. Area of the square is a^2 = (\frac{\pi r}{2})^2 = \frac{\pi^2 r^2}{4}. The ratio is \frac{\pi r^2}{\frac{\pi^2 r^2}{4}} = \frac{4}{\pi}, which is 4:\pi.

Related questions on Mensuration

• A pendulum swings through an angle of 30° and its end describes an arc of length 55 cm. What is the length of the pendulum? (Take $\pi = 22/...
• A conical tent has an angle of 60° at the vertex. If the curved surface area is 100 m^2, then what is the volume of the tent?
• A right circular cone and a hemisphere have equal base and equal volume. What is the ratio of the height of the cone to the radius of the he...
• A wire is in the form of an equilateral triangle with an area of 36\sqrt{3} cm^2. If it is changed into a semicircle, then what is its r...
• Let the area of the largest possible square inscribed in a circle of unit radius be x. Let the area of the largest possible circle inscribed...