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Math Help - Calc word problem

  1. #1
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    Calc word problem

    All edges of a cube are expanding at a rate of 3 centimeters per second.
    (a) How fast is the volume changing when each edge is 4 centimeter(s)?

    (b) How fast is the volume changing when each edge is 9 centimeters?
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  2. #2
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    Quote Originally Posted by tradar View Post
    All edges of a cube are expanding at a rate of 3 centimeters per second.
    (a) How fast is the volume changing when each edge is 4 centimeter(s)?

    (b) How fast is the volume changing when each edge is 9 centimeters?
    Let a denote the edge of the cube. Then

    V = a^3

    That means:

    \dfrac{dV}{dt} = 3a^2 \cdot \dfrac{d a}{dt}

    You already know a = 4\, cm\, \text{and } \dfrac{d a}{dt} = 3 \frac{cm}s

    I've got \dfrac{dV}{dt} = 144\,\frac{cm^3}{s}

    b) has to be done in just the same way. I leave this part for you.
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