Eric Nicholas K's answer to Manoj's Junior College 1 H2 Maths Singapore question.
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Here are my workings for this question. We use similar triangles to express the radius of the water level r at time t in terms of the height h of the water level at the same instant.
From there, we work out the volume of water remaining in the cone, derived by subtracting the volume of the smaller cone from the full cone. We express this volume remaining in terms of only the height h.
From there, we just form the rates of change equation and solve for dh/dt.
From there, we work out the volume of water remaining in the cone, derived by subtracting the volume of the smaller cone from the full cone. We express this volume remaining in terms of only the height h.
From there, we just form the rates of change equation and solve for dh/dt.
Date Posted:
4 years ago
Or you can just find the ratio of the sides to be (12 - h)/12
Then ratio of volume = ((12 - h)/12)³
(12 - h)³/1278
volume of water = ⅓π(4²)(12) -⅓π(4²)(12) (12 - h)³/1278
= 64π - π/27 (12 - h)³
Then ratio of volume = ((12 - h)/12)³
(12 - h)³/1278
volume of water = ⅓π(4²)(12) -⅓π(4²)(12) (12 - h)³/1278
= 64π - π/27 (12 - h)³
Thank u so muc sir/mam.
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