## Friday, July 20, 2012

### Problem of the Week Day 5: Week of 7/16/12 - 7/20/12

Today is the final day of the problem of the week! Remember to email me your answers at Ethan@EthanMath.com. Don't forget that you must substitute in your answers from previous days. The answer will never contain a variable in it.

Easy: As usual, I like to finish off the week with a little geometry. Pretend we have a circle. It's circumference is below:

C = n√(π)

From that fact, determine the area A of the circle.

Hint: The formulas for circumference and area are below. The letter r stands for the radius, which is found in both formulas.

C = 2πr
A = πr^2

Hard: I have two shapes: a square and a circle. Their areas are below:

A(square) = s^2/2
A(circle) = πx

Figure out which shape is bigger. Then, find the perimeter of that shape.

P =

Hint: The circle's formulas are in the easy problem. The square's are (with s standing for side):

A = s^2
P = 4s

It may make it more complicated, but you can figure out which shape is bigger without multiplying the π and the x together. If you want to figure it out that way, determine the diameter of the circle and the diagonal length of the square (which is simple using the Pythagorean Theorem). Simple logic from there will determine their size.

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