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().
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().
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text: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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