Connected rates of change?

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Connected rates of change?

A watermelon is assumed to be spherical in shape while it is growing. Its mass $M kg$ , and radius r $cm$ , are related by the formula $M = kr^3$ , where k is a constant. It is also assumed that the radius is increasing at a constant rate of 0,1 $cm$ per day. On a particular day the radius is $10 cm$ and the mass is 3,2 $kg$ . Find the value of $k$ and the rate at which the $mass$ is increasing on this day.

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Answer 1 · 2017-08-03T10:30:22

$k=2/625,(dM)/dt=0.096" Kg/day"$

Explanation:

$M=kr^3$

$"given "r=10" and "M=3.2$

$rArrk=M/r^3=3.2/1000=2/625$

$(dM)/dt=(dM)/(dr)xx(dr)/dtlarr" chain rule"$

$"where "(dM)/(dr)=3kr^2" and "(dr)/dt=0.1$

$rArr(dM)/dt=3xx2/625xx(10)^2xx0.1$

$color(white)(rArr(dM)/dt)=0.096" Kg/day"$

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Connected rates of change?

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