1. Sticky Chins' Ice Cream shop uses an ice cream cone that with a maximum radius...

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1. Sticky Chins' Ice Cream shop uses an ice cream cone that with a maximum radius of 1 inch and a height of 4 inches. - r=1 h=4 (a) Given the cone is completely full and the ice cream above the cone creates a hemisphere, find the volume of the ice cream using an in- tegral, rotating around the vertical center of the cone as indicated in the diagram. (b) Suppose Sticky Chins' wants to design a cone with the same height as their current cone but in such a way that one cup (14.5 cubic inches) of ice cream is served. Find the radius needed for such a cone. Give your answer as a decimal approximation using evalf(). 1. Sticky Chins' Ice Cream shop uses an ice cream cone that with a maximum radius of 1 inch and a height of 4 inches. - r=1 h=4 (a) Given the cone is completely full and the ice cream above the cone creates a hemisphere, find the volume of the ice cream using an in- tegral, rotating around the vertical center of the cone as indicated in the diagram. (b) Suppose Sticky Chins' wants to design a cone with the same height as their current cone but in such a way that one cup (14.5 cubic inches) of ice cream is served. Find the radius needed for such a cone. Give your answer as a decimal approximation using evalf().

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a To find the volume of the ice cream using an integral we can use the method of cylindrical shells ... View the full answer