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Bladerunner1122

  • 3 years ago

A sphere is increasing in volume at the rate 3pi cm^3/s. At what rate is its radius changing when the radius is 1/2 cm?

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  1. sauravshakya
    • 3 years ago
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    V=4/3 pi r^3 dV/dt=d(4/3pi r^3)/dt

  2. sauravshakya
    • 3 years ago
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    Now, use chain rule to find dr/dt

  3. sauravshakya
    • 3 years ago
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    can u?

  4. Bladerunner1122
    • 3 years ago
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    dr/dt = 1/(4pi r^2) * (dV/dt)

  5. Bladerunner1122
    • 3 years ago
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    Substitute 1/2 in for r?

  6. sauravshakya
    • 3 years ago
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    yes

  7. sauravshakya
    • 3 years ago
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    and dV/dt=3pi cm^3/s

  8. Bladerunner1122
    • 3 years ago
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    dr/dt = 1/(4pi*((1/2)^2))*3pi cm^3/s = 3 cm^3/s Thank you!! :)

  9. sauravshakya
    • 3 years ago
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    welcome

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