Another word problem!

**lilikoipssn** · April 8th 2008, 08:47 PM

A circle and a square have the same area. Find the length of the diagonal of the square divided by the radius of the circle. (Hint: draw a diagram and label unknowns.)

**TheEmptySet** · April 8th 2008, 09:14 PM

Originally Posted by lilikoipssn

A circle and a square have the same area. Find the length of the diagonal of the square divided by the radius of the circle. (Hint: draw a diagram and label unknowns.)

Since they have the same area we know.

$A=\pi r^2 \mbox{ and } A=s^2 \iff \pi r^2=s^2 \iff r^2=\frac{s^2}{\pi}$

$r=\frac{s\sqrt{2}}{\sqrt{\pi}}$

Now using the pythagorean theorem we know the length of the diagonal is

$d^2=s^2+s^2 \iff d^2 =2s^2 \iff d=s\sqrt{2}$

Now we are asked to find the ratio of diagonal to the radius

$\frac{s\sqrt{2}}{\frac{s\sqrt{2}}{\sqrt{\pi}}}=\sq rt{\pi}$

Thread: Another word problem!

LinkBack

Thread Tools

Display

Another word problem!

Similar Math Help Forum Discussions

word problem - the snow plough problem?

Weird Trig Angle of Elevation problem + Azimuth Word Problem

1 Word problem and 1 function problem

Volume Word Problem (geometry-type problem for physics)

Search Tags