Suppose that both the radius r and height h of a circular cone are increasing at a rate of 7 cm/s. How fast is the volume of the cone increa

Question

Suppose that both the radius r and height h of a circular cone are increasing at a rate of 7 cm/s. How fast is the volume of the cone increasing when r=15 cm and h=10 cm?

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Samantha 1 week 2021-09-13T02:51:55+00:00 1 Answer 0

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    2021-09-13T02:52:56+00:00

    Answer:

    The volume of the cone is increasing at the rate oof 3848.45 cm³/s when r=15 cm and h=10 cm.

    Step-by-step explanation:

    The volume of the cone is given by the following formula:

    V = \frac{r^{2}h\pi}{3}

    In which V is measured in cm³ while r and h are measured in cm.

    Suppose that both the radius r and height h of a circular cone are increasing at a rate of 7 cm/s.

    This means that \frac{dh}{dt} = \frac{dr}{dt} = 7

    How fast is the volume of the cone increasing when r=15 cm and h=10 cm?

    This is \frac{dV}{dt} when r = 15, h = 10.

    V = \frac{r^{2}h\pi}{3}

    Applying implicit differentiation:

    We have three variables, V, r and h. So

    \frac{dV}{dt} = \frac{2r\frac{dr}{dt}h \pi + r^{2}\pi \frac{dh}{dt}}{3}

    \frac{dV}{dt} = \frac{2*15*7*10\pi + 225*\pi*7}{3}

    \frac{dV}{dt} = 3848.45

    The volume of the cone is increasing at the rate oof 3848.45 cm³/s when r=15 cm and h=10 cm.

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