Informal Argument for Volume of Sphere
Geometry · Flashcards
GEOMETRY · FLASHCARDS
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QUESTION
What is the base radius of the cone in the classic hemisphere Cavalieri argument?
QUESTION
Simplify the cross-section area
c
0
r
2
−
c
0
x
2
c^0r^2-c^0x^2
c
0
r
2
−
c
0
x
2
.
QUESTION
Identify the solid used with Cavalieri to derive
V
=
4
3
π
r
3
V=\frac{4}{3} \pi r^3
V
=
3
4
π
r
3
for a sphere.
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ANSWER
A hemisphere compared to a cylinder minus a cone. Classic Cavalieri setup comparing hemisphere to cylinder minus cone.
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