Dimensions:

Problem Statement:

The curved boundaries of the shape shown are quarter circles. Given the dimensions above, find:

the $x$ location of the centroid of the shape,

the $y$ location of the centroid of the shape,

the Second Moment of Area of the shape about the $x$ axis,

the Second Moment of Area of the shape about the $y$ axis

the Second Moment of Area of the shape about a horizontal axis passing through the centroid of the shape

the Second Moment of Area of the shape about a vertical axis passing through the centroid of the shape

Answers:

$x_{\text{c}\text{e}\text{n}\text{t}\text{r}\text{o}\text{i}\text{d}}=$

$y_{\text{c}\text{e}\text{n}\text{t}\text{r}\text{o}\text{i}\text{d}}=$

$I_x=$

$I_y=$

$I_{x_{NA}}=$

$I_{y_{NA}}=$