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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
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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) = , and
for the cone C(Z) = .
They want you find z such that S(z) = C(z), or, which is the same
= ,
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) = (red) and C(z) = (green)
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Final notice. It is difficult to imagine the two solids of this size standing on a table.