Find Centroid: Solve Homework Statement

[suspenc3]

Homework Statement

http://img170.imageshack.us/img170/214/centroidssk4.th.jpg [Broken]

Homework Equations

$$\bar{Y}A_{TOT}=\bar{Y_1}A_1+\bar{Y_2}A_2+\bar{Y_3}A_3$$

The Attempt at a Solution

by observation:

$$\bar{Y_1}=7.5mm$$
$$\bar{Y_2}=82.5mm$$
$$\bar{Y_3}=215mm$$
$$A_1=(15mm)(150mm)=2250mm^2$$
$$A_2=(15mm)(150mm)=2250mm^2$$
$$A_3=(\pi)(50mm^2)=7854mm^2$$

$$A_{TOT}=12354mm^2$$

$$\bar{Y}=\frac{1891110mm^3}{12354mm^2}$$

$$\bar{Y} = 153.1mm$$

The book says the answer is 154mm, I know that its not off by far but am I doing something wrong, or is the book rounding off somewhere? I am slightly off on every single question I attempt!

 

[Doc Al]

$$\bar{Y_2}=82.5mm$$

Correct this one.

 

[suspenc3]

Righhhht, Dumb Mistake

Thanks