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16 September, 00:08

The radius of a spherical balloon being filled with air expands at 4 cm^3 per minute. Assuming the balloon fills in spherical shape, how fast is the radius of the spherical balloon increasing in cm per minute after 2.25 minutes?

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  1. 16 September, 00:12
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    Answer: dr/dt = 0.042 cm/minute

    Step-by-step explanation:

    Given;

    dV/dt = 4cm^3/minute

    t = 2.25minutes

    Volume of a sphere is given as;

    V = (4/3) πr^3

    Change in Volume ∆V can be derived by differentiating the function.

    dV/dt = 4πr^2. dr/dt

    dV/dt = 4πr^2dr/dt ... 1

    dV/dt is given as 4 cm^3/min

    radius after 2.25 minutes can be gotten from the the volume.

    Volume after 2.25mins = 4*2.25 = 9cm^3

    9cm^3 = V = 4/3πr^3

    r^3 = 27/4π

    r = (27/4π) ^1/3

    From equation 1.

    dr/dt = (dV/dt) / 4πr^2 = 4 / (4πr^2) = 1 / (πr^2)

    dr/dt = 1 / (π (27/4π) ^2/3)

    dr/dt = 0.042cm/minute.
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