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calculus

A potter forms a piece of clay into a right circular cylinder. As she rolls it, the height h of the cylinder increases and the radius r decreases. Assume that no clay is lost in the process. Suppose the height of the cylinder is increasing by 0.5 centimeters per second. What is the rate at which the radius is changing when the radius is 3 centimeters and the height is 8 centimeters?

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  1. So the volume is a constant ----> d(volume)/dt = 0

    V = πr^2 h
    given: dh/dt = .5 cm/s
    find: dr/dt when r = 3 and h = 8

    dV/dt = πr^2 dh/dt + h(2πr) dr/dt
    0 = π(9)(.5) + 8(6π)dr/dt
    dr/dt = -4.5π/48π = -3/32 cm/s

    the radius is decreasing at a rate of 3/32 cm/s

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  2. THANK U!!!!!!

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  3. efewkfnwe

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  4. A potter forms a piece of clay into a circular cylinder. As he rolls it, the length, L, of the cylinder increases and the radius, r, decreases. If the length of the cylinder is increasing by 0.2 cm per second, find the rate at which the radius is changing when the radius is 4 cm and the length is 10 cm.

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