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secondary 4 | A Maths
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(i) show that the volume of the object is given by V=12(pi)(r) - ⅔(pi)(r)³
(ii) given that r can vary, find the value if r for which V has a stationary value
(iii) calculate the stationary value of V and determine if the volume has a maximum or minimum
help please above are the questions thank you!
Date Posted: 7 months ago
Views: 67
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Part 1/2 of solution.
Date Posted:
7 months ago
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Part 2/2 of solution.
First, express the total surface area of figure in terms of h and r and equate to 24pi.
Then express h in terms of r since the volume to be shown is in terms of r.
Then express volume of figure in terms of h and r and sub the expression of h into it.
Then differentiate w.r.t r. Equate dV/dr=0 and you will get 2 values.
In fact, r cannot take negative value. So the negative value can be rejected. So the volume is a maximum when r takes the positive value.
Hope this helps :)
First, express the total surface area of figure in terms of h and r and equate to 24pi.
Then express h in terms of r since the volume to be shown is in terms of r.
Then express volume of figure in terms of h and r and sub the expression of h into it.
Then differentiate w.r.t r. Equate dV/dr=0 and you will get 2 values.
In fact, r cannot take negative value. So the negative value can be rejected. So the volume is a maximum when r takes the positive value.
Hope this helps :)
Date Posted:
7 months ago
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