# How do you find the centroid of the quarter circle of radius 1 with center at the origin lying in the first quadrant?

##### 1 Answer

Non-Calculus Solution:

Observation 1:

The centroid must lie along the line

Observation 2:

For some constant,

Observation 3:

Since the area of the quarter circle (with radius =

the line

The area of the triangle formed by the X-axis, the Y-axis, and

is

Therefore

and the centroid is located at the midpoint of the line segment