The Volume Formula of a Sphere
Picture a marble and a beach ball. Which one would you describe as a sphere? What differences between the two could possibly impact how we describe what a sphere is?
Use your knowledge about the volumes of cones and cylinders to find a volume for a solid hemisphere of radius R.
SPHERE: Given a point 𝐶 in the three-dimensional space and a number 𝑟 > 0, the sphere with center 𝐶 and radius 𝑟 is the set of all points in space that are distance 𝑟 from the point 𝐶.
SOLID SPHERE OR BALL: Given a point 𝐶 in the three-dimensional space and a number 𝑟 > 0, the solid sphere (or ball) with center 𝐶 and radius 𝑟 is the set of all points in space whose distance from the point 𝐶 is less than or equal to 𝑟.
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