A single-scoop ice cream cone is a composite body made from a single scoop of ic

ID: 1862939 • Letter: A

Question

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=1.58in that is placed into a 4.00in tall cone. The interior height of the cone is 3.60in . The cone has an exterior radius of 1.25in and an interior radius of 1.10in . The scoop of ice cream sits on the cone's interior radius and extends into the cone some distance. Find the z

Explanation / Answer

volume of sphere = (4/3)*pi*r^3 = (4/3)*pi * 1.58^3 = 16.52189547 in^3

Let angle from center of sphere to the point of contact with cone makes theeta angle from vertical.

so... sin theeta = ( 1.25 / 1.58 )

so... theeta = 52.292103

so... height of center of sphere above the base of cone = 1.58 * cos theeta = 0.966385 inch

centroid of sphere = 4 + 0.966385 = 4.966385 inch

volume of cone = (1/3)*pi*[ 1.25^2 *4 - 1.1^2*3.6 ) = 1.98339216 in^3

centroid of solid cone is h/4 from the base....

so... for the outer solid cone.... centroid distance = (4*3/4)

for inner cone... centroid distance = (0.4 + (3.6*3/4) )

so.. centroid of cone = [(1/3)*pi*( 1.25^2 *4*(4*3/4) - 1.1^2*3.6*(0.4 + (3.6*3/4) ) ] / [ (1/3)*pi*[ 1.25^2 *4 - 1.1^2*3.6 ) ] = 2.77 inch ...

so.... z_bar = [ volume_sphere * z_sphere + volume_cone*z_cone ] / [ volume_cone + volume_sphere ]

so... z_bar = [ (16.52189547*4.966385) + ( 1.98339216*2.77) ] / [ 16.52189547 + 1.98339216] = 4.731 inch

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A single-scoop ice cream cone is a composite body made from a single scoop of ic

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A single-scoop ice cream cone is a composite body made from a single scoop of ic

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