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26 February, 13:51

A thin metal disk is heated altering its size, but not its shape. As the disk is heated its radius increases at a rate of 0.04 mm/sec. How fast is the disk's area changing when the radius is 225 mm

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  1. 26 February, 14:12
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    Given Information:

    Radius of disk = r = 225 mm

    Rate of change of radius = dr/dt = 0.04 mm/s

    Required Information:

    Rate of change of area = dA/dt = ?

    Answer:

    Rate of change of area = 56.54 mm²/s = 5.7x10⁻⁵ m²/s

    Explanation:

    Assuming that the disk is circular shaped then the area of disk is given by

    A = πr²

    Where r is the radius of the disk.

    Differentiating the area with respect to time t

    dA/dt = πr²

    dA/dt = 2πrdr/dt

    Where dr/dt is the rate of change of radius

    dA/dt = 2π*225 * (0.04)

    dA/dt = 56.54 mm²/sec

    or in standard units

    (0.04 mm/s) / 1000 = 4.0x10⁻⁵ m/s

    (225 mm) / 1000 = 0.225 m

    dA/dt = 2π*0.225 * (4.0x10⁻⁵)

    dA/dt = 5.7x10⁻⁵ m²

    Therefore, the area of the disk is changing at the rate of 5.7x10⁻⁵ m²/s
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