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junior college 1 | H2 Maths
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I really need ur help. Would really appreciate the help.
Date Posted: 5 years ago
Views: 329
The space above the water has a shape of a cone. This cone shape is similar to the container cone itself.
If you take the front view it's actually 2 similar triangles. Use the ratios for similar triangles to find the cone space's radius. Its height is just 12 - h.
Find its volume and subtract it from the capacity of the container to get the answer
If you take the front view it's actually 2 similar triangles. Use the ratios for similar triangles to find the cone space's radius. Its height is just 12 - h.
Find its volume and subtract it from the capacity of the container to get the answer
Oh thank you so much?
Or you can just use ratio of volume directly, which is faster
Volume of container = ⅓πr²h
= ⅓π(4²)(12)
= 64π
Ratio of sides of the similar cones
= (12 - h)/12
Ratio of volume = ((12 - h)/12)³
= (12 - h)³/1728
Volume of water
= 64π - 64π((12 - h)³/1278)
= 64π - π/27 (12 - h)³
Volume of container = ⅓πr²h
= ⅓π(4²)(12)
= 64π
Ratio of sides of the similar cones
= (12 - h)/12
Ratio of volume = ((12 - h)/12)³
= (12 - h)³/1728
Volume of water
= 64π - 64π((12 - h)³/1278)
= 64π - π/27 (12 - h)³
See 1 Answer
done
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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:
5 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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