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.

1 Answer
Jim G.
Aug 3, 2017

#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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