Concept explainers
To derive : the formula of volume of a hemisphere.
Explanation of Solution
Given information : The volume of a hemisphere of radius
has been removed as suggested by the figure:
The hemisphere cross sectional area is given by:
The cross section of the right circular cylinder with cone removed is
Since these area are equal, the volumes of the solid formed are equal by cavalier’s theorem. Therefore, the volume of the hemisphere is given by the volume of the cylinder less the volume of the cone.
Chapter 8 Solutions
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
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