SOLUTION: a sphere of 10 m and a right circular cone of base radius 10 m and height 15 m stands on a table. at what height from the table should the two solids be cut in order to have equal

Algebra ->  Bodies-in-space -> SOLUTION: a sphere of 10 m and a right circular cone of base radius 10 m and height 15 m stands on a table. at what height from the table should the two solids be cut in order to have equal      Log On


   

Question 1085987: a sphere of 10 m and a right circular cone of base radius 10 m and height 15 m stands on a table. at what height from the table should the two solids be cut in order to have equal circular sections
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
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a sphere of highlight%28the_radius%29 10 m and a right circular cone of base radius 10 m and height 15 m stands on a table.
at what height from the table should the two solids be cut in order to have equal circular sections
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Let "z" be the vertical coordinate/axis starting (z=0) at the table and directed vertically up.


Then the horizontal section area at elevation z is:

    for the sphere S(z) = pi%2A%2810%5E2-%2810-z%29%5E2%29,   and

    for the cone   C(Z) = pi%2A%2810%2A%28%2815-z%29%2F15%29%29%5E2.


They want you find z such that S(z) = C(z),  or,  which is the same

pi%2A%2810%5E2-%2810-z%29%5E2%29 = pi%2A%2810%2A%28%2815-z%29%2F15%29%29%5E2,


I will leave the solution of this equation to you.


Instead, I'll give you the plots of the two functions S(z) and C(z).




Plots S(z) = pi%2A%2810%5E2-%2810-z%29%5E2%29 (red) and C(z) = pi%2A%2810%2A%28%2815-z%29%2F15%29%29%5E2 (green)


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Final notice. It is difficult to imagine the two solids of this size standing on a table.