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=1.58 in. that is placed into a 4.00 in. tall cone. The interior height of the cone is 3.60 in. The cone has an exterior radius of 1.25 in. and an interior radius of 1.10 in. The scoop of ice cream sits on the cone's interior radius and extends into the cone some distance. Find the "z bar" centroid for the cone (the scoop of ice cream and the cone). The image depicts a geometric model of an ice cream cone with an attached spherical scoop. The model includes the following measurements:- A sphere representing the ice cream scoop with a radius labeled as \( r \).- A cone representing the cone of the ice cream with a height of \( 4.00 \) inches.- The base radius of the cone is \( 1.25 \) inches.Axes are labeled as \( x \), \( y \), and \( z \), suggesting a three-dimensional coordinate system is used for positioning.This diagram is useful for analyzing the relationship between the cone and the sphere, as well as for calculating various geometric properties such as volume and surface area.

Radius of the sphere is r=1.58 in Height of the solid cone is h0=4 in Radius of the solid cone is…

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A single-scoop ice cream cone is a composite

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

The image depicts a geometric model of an ice cream cone with an attached spherical scoop. The model includes the following measurements:

- A sphere representing the ice cream scoop with a radius labeled as \( r \).
- A cone representing the cone of the ice cream with a height of \( 4.00 \) inches.
- The base radius of the cone is \( 1.25 \) inches.

Axes are labeled as \( x \), \( y \), and \( z \), suggesting a three-dimensional coordinate system is used for positioning.

This diagram is useful for analyzing the relationship between the cone and the sphere, as well as for calculating various geometric properties such as volume and surface area.

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