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In: Physics

At an Ice Cream Store, a single scoop of ice-cream can be modeled by a hemisphere...

At an Ice Cream Store, a single scoop of ice-cream can be modeled by a hemisphere which is 1 inch tall. The ice-cream fits perfectly on top of a cone that is 4 inches tall and has a 1 inch radius at the top.

1. Write one equation in Cartesian coordinates (x, y, z) to describe the scoop and one equation for the cone.

2. If the mass of one scoop of ice cream is 60 grams and that the mass density of ice-cream is constant, find the mass density of the ice-cream.

3. Find the center of mass of the scoop of ice-cream

4. Compute the total surface area of the ice-cream scoop and the cone

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