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Math Help - rate of change according to time problem

  1. #1
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    rate of change according to time problem

    A prism of an equilateral triangle base , its height is triple the length of its base if the length of its base increases by rate 0.01 cm/sec . Find the rate of increase of volume of the prism at length of base 5 root3 cm
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  2. #2
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    Re: rate of change according to time problem

    I'm not sure what you mean by "the length of its base". The obvious thing is the length of a side of the triangle but another possibility is the length of an altitude.

    First, can you write the formula for volume of such a prism with base side length s and height h?
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  3. #3
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    Re: rate of change according to time problem

    Quote Originally Posted by HallsofIvy View Post
    I'm not sure what you mean by "the length of its base". The obvious thing is the length of a side of the triangle but another possibility is the length of an altitude.

    First, can you write the formula for volume of such a prism with base side length s and height h?
    the base length means -->the length of a side of the triangle

    here is my attempt :

    volume of prism = area of base * height .....assume that base length = x ,, height of prism = h = 3x
    so
     v= (\frac{1}{2} \times X \times \frac{\sqrt{3}}{2}X )\times 3X
    v = \frac{3 \sqrt{3}}{4} \times x^3 by taking derivative with respect to time
    so
     \;\frac {dv}{dt} = \frac{9 \sqrt{3}}{4} \times x^2 \times \frac{dx}{dt} by substituting i found that
     \frac {dv}{dt} = \frac{27 \sqrt{3}}{16}

    is that right?????
    Last edited by mido22; March 3rd 2013 at 12:08 PM.
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