Part C

Learning Goal:

A centroid is an object's geometric center. For an object of uniform composition, its centrold is also its center of mass. Often the centroid of a complex composite body is found by$,$ first, cutting the body into regular shaped segments, and then by calculating the weighted average of the segments' centroids. An object is made from a uniform piece of sheet metal. The object has dimensions of $a=1\mathrm{.}25ft,$ where $a$ is the diameter of the sem$-$circle, $b=3\mathrm{.}67ft,$ and $c=2\mathrm{.}40ft.$ A hole with diameter $d=0\mathrm{.}750$ ft is centered at $(1\mathrm{.}03,0\mathrm{.}625)$

Figure

$1$ of $2$

Find $\frac{?}{\text{b}\text{a}\text{r}}(y),$ the $y-$coordinate of the body's centroid. $($Figure$,1)$

Express your answer numerically in feet to three significant figures.

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Part D

A single$-$scoop ice cream cone is a composite body made from a single scoop of ice cream placed into a cone. $($Figure $2)$ Assume that the scoop of ice cream is a sphere with radius $r=1\mathrm{.}64$i placed into a $4\mathrm{.}00$ in tall cone. The interior height of the cone is $3\mathrm{.}60$ in$.$ The cone has an exterior radius of $1\mathrm{.}25$ in and an interior radius of $1\mathrm{.}10$ in$.$ The scoop of ice cream sits on the cone's radius and extends into the cone some distance. Find the $\frac{?}{\text{b}\text{a}\text{r}}(z)$ centroid for the cone $($the scoop of ice cream and the cone$).$

Express your answer numerically in inches to three significant figures.

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