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MATHEMATICS OBJECTIVE
Students will be able to:
Calculate the volume of a sphere.
Recognize the relationship between the formula for the volume of a cone and the volume of a sphere.
ESSENTIAL UNDERSTANDING
The volumes of a sphere and cone are proportionally related. The volume of a sphere of radius r is twice the volume of a cone with height 2r and radius r. From this relationship, the formula for the volume of a sphere can be deduced.
I can calculate the volume of a sphere.
I can relate the volume of a sphere to the volume of a cone.
VOLUME OF A SPHERE
The volume of a sphere is twice the volume of a cone that has the same
circular base and height. The formula for the volume of a sphere with
radius r is V = (4/3)πr³.
FORMULA
V = (4/3)πr³
DIAGRAM DESCRIPTION
A blue sphere shows a center point and a dashed radius labeled r,
with curved and dashed lines indicating the circular cross-section.
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