The radius of a cone is r cm and its height is h cm. the change in volume when the height is decreased by x cm is the same as the change in volume when radius is decreased by x cm. find the relation between x, r and h ?
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Answer:
Given
dt
dr
=1 and
dt
dh
=−1
We know that, Volume of a cylinder is given by
V=πr
2
h
⟹
dt
dV
=π2rh
dt
dr
+πr
2
dt
dh
⟹
dt
dV
=πr(2h(1)+r(−1))
=π×5(2×15−5)
=125π
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