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Calculus

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A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.2 cm/min. At what rate is the volume of the snowball decreasing when the diameter is 16 cm.

  • Calculus - ,

    The diameter of the sphere is decreasing at 0.2 cm/min. This means that its radius is decreasing by 0.1 cm/min.

    The formul

  • Calculus - ,

    The diameter of the sphere is decreasing at 0.2 cm/min. This means that its radius is decreasing by 0.1 cm/min. We also know its current radius is 8 cm.

    The formula for the volume of a sphere is:
    V= (4/3)*Pi*r^3

    So, we can calculate the volume difference in 1 minute, by subtracting its volume after one minute from its current volume:

    Vc-Vf = [(4/3)*Pi*(8 cm)^3] -
    [(4/3)*Pi*(8-0.1 cm)^3]
    = 2144.66 cm^3- 2065.24 cm^3= 79.42 cm^3

    This means its volume is decreasing by 79.42 cm^3/min

  • Calculus - ,

    Hmm. I tried that and it wasn't correct.

  • Calculus - ,

    The answer is 80.4248 cm^3/min.
    (1/3)(4π)(1/8)(3(16)²)(-0.2)

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