Eric Nicholas K's answer to huihuibuhui's Secondary 4 A Maths Singapore question.
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We need to know these to be able to solve this question
- volume of pyramid in general
- an understanding that for regular shaped containers, the side surfaces are designed such that similar triangles can be seen (as I illustrated in the diagram)
- being able to express the volume of the pyramid as a single variable only
- using the chain rule formula dV/dt = dV/dh times dh/dt
- volume of pyramid in general
- an understanding that for regular shaped containers, the side surfaces are designed such that similar triangles can be seen (as I illustrated in the diagram)
- being able to express the volume of the pyramid as a single variable only
- using the chain rule formula dV/dt = dV/dh times dh/dt
Date Posted:
3 years ago
Omg, i just realized my mistake. Thank you so much. :)
Wait
Volume of container
= 1/3 x (2L)^2 x h
I defined L as “half the length” of the container. So 2L is the length. And not L, which I have used in my formula.
An error on my part. The other tutor is correct.
I update my workings later if I have time, since I am jam packed with my schedule at the moment.
Volume of container
= 1/3 x (2L)^2 x h
I defined L as “half the length” of the container. So 2L is the length. And not L, which I have used in my formula.
An error on my part. The other tutor is correct.
I update my workings later if I have time, since I am jam packed with my schedule at the moment.
You can append this to my working.
Volume of pyramid
= 1/3 x (2L)^2 x h
= 4/3 * L^2 * h
= 4/3 * (3/10)^2 * h
= 3/25 h^3
dV/dh = 9/25 h^2
When h = 10, dV/dh = 36 cm^2
Then,
dV/dt = dV/dh * dh/dt
5 = 36 * dh/dt
dh/dt = 5/36 cm/s
Volume of pyramid
= 1/3 x (2L)^2 x h
= 4/3 * L^2 * h
= 4/3 * (3/10)^2 * h
= 3/25 h^3
dV/dh = 9/25 h^2
When h = 10, dV/dh = 36 cm^2
Then,
dV/dt = dV/dh * dh/dt
5 = 36 * dh/dt
dh/dt = 5/36 cm/s
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