Original
Next, we {{CMD_31}}draw a picture{{CMD_32}}. Note that our pizza dough is shaped as a cylinder.
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Next we need to {{CMD_36}}find equations{{CMD_37}}. Recall the formula for the volume of the cylinder, {{MATH_38}} and note that {{MATH_39}}, and write
{{MATH_40}}
which immediately simplifies to
{{MATH_41}}
Since both {{MATH_42}} and {{MATH_43}} are functions of time, we now {{CMD_44}}differentiate{{CMD_45}} both sides of the equation using implicit differentiation,
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Now we'll {{CMD_47}}evaluate{{CMD_48}} all the quantities at the instant when {{MATH_49}}.
But, first, we have to compute {{MATH_50}} at that moment. Since
{{MATH_51}} it follows that {{MATH_52}}, when {{MATH_53}}. Now, we are ready to {{CMD_54}}solve{{CMD_55}}.
{{MATH_56}}
{{MATH_57}}
Therefore, when {{MATH_58}},
{{MATH_59}}
Hence, the thickness of the dough is changing at a rate of {{MATH_60}}
cm/min when {{MATH_61}} cm.
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In our next example we consider a melting snowball.
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Consider a melting snowball.