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Solve the given problems.A conical paper cup has a slant height of $10.0 \mathrm{cm}$. Express the volume $V$ of the cup in terms of $\theta / 2,$ where $\theta$ is the vertex angle at the bottom of the cup. Then find $d V / d \theta$

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 1

Derivatives of the sine and Cosine Functions

Derivatives

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Slant height and cones Amo…

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Here we have a conical paper cup with a slant height of 10 cm to want to express the volume of the cup. In terms of the angle theta over to where data is the vertex angle at the bottom of the cup. And then we want to find DVD data so we know that the cup, if we look at the volume of a cone, the cup is going to be pi r squared H over three. So volume equals high, R squared Age over three. What we have to do in this problem is recognized at the height and the radius have a relationship. Um In terms of the angle measurement, if we have a high greater height and a smaller radius, then we have a much larger angle degree. But if we have a smaller height and a wider radius than that changes things, so we see that the radius and the height, this is the opposite and adjacent. So theta is equal to be inverse tangent or the arc tangent of the opposite, which is the height over the radius. So, by creating this relationship were able to rephrase the volume in terms of the value of data.

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