Question

a circle is circumscribed about a square. if the sides of the square are 3, what is the approximare circumference of the circle? Round your answer to the tenths place.

A. 18.8
B. 13.3
C. 9.4
D. 28.3

Answer 1

Hi Ira,

To solve this one you need to know the radius of the circle.

To get the radius, you divide the square into 4 triangles by drawing in the diagonals. The distance from the point of intersection of the diagonals to the corner is the radius of the circle.

So by doing this, the base and height of one of these triangles is 1.5; using Pythagoras' Theorem we get the hypotenuse (or radius) to be 2.12132...

Then the formula for the circumference of a circle is just 2r*pi.

Tell me what you get :)

Answer 2

so 2(2.12132)pi?

Answer 3

13.32

Answer 4

Yep that's it. Just remember with those type of questions: What do I want to find out? How can I get there?
For this one you wanted the circumference, to get it you need the radius, and the only info given is the side lentghy of the square. It may not seem obvious at first, but with some intuition you will get the answer.

Answer 5

13.32