A cylinder contains 150.8 cubic units of water. What is the minimum radius of a sphere that will hold the water?

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Answer 1 · 2017-06-29T23:26:17

#r = 3.3 " units"#

Given: #V_("cylinder") = 150.8 " units"^3#

The volume for a sphere: #V_("sphere") = 4/3 pi r^3#

Set the two equations equal and solve for the radius:

#4/3 pi r^3 = 150.8#

#3/4 * 4/3 pi r^3 = 150.8/1 * 3/4#

#pi r^3 = 113.1#

#pi/(pi) r^3 = 113.1/(pi)#

#r^3 = 36.00#

#root(3)(r^3) = root(3)(36)#

#r = 3.3 " units"#