WEBVTT
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So we want to know, Um, how much
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paint Approximately would be needed to apply a coat to
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a hemispherical dome. So we know that the volume
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of the hemispherical dome is one half of the volume
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of us here. So if the volume of a
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sphere is four thirds pi r cubed, we know
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that the volume we're focusing on is two thirds pi
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r cubed. Then taking the derivative of this,
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we get that devi d r is equal to two
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pi r squared and then putting the derivative into differential
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form. We get that DV equals two pi r
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squared d r. Now the reason why we want
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to do this is because we know that are is
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the original radius before paint is applied, d r
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is similar to delta are or the change in the
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radius which we know is going to be 0.5 Then
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when we plug in these values, we get that
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DV equals two pi 25 meters time, 0.0 05
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m because we converted it from centimeters which is equal
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to 1.96 m cubed eso that right there would be
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the volume of paint or the amount of paint needed
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to cover the hemispherical dome