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Sagot :
The volume of the rind is growing at the rate 681.097 cubic centimeters per week at the end of the fifth week.
In the given question, the radius of a spherical watermelon is growing at a constant rate of 2 centimeters per week.
The thickness of the rind is always one tenth of the radius.
We have to find the volume of the rind is growing at the rate cubic centimeters per week at the end of the fifth week.
Assume that the radius is initially zero.
Let r be the radius of watermelon.
dr/dt = 2 cm/week
Radius after 5 week = 10 cm
Thickness of the rind = r/10 cm = 0.1r cm
Now the volume of rind
V = 4/3 π[r^3-(0.9r)^3]
dV/dt = 4/3 π[3r^2-3r^2(0.9)^3]dr/dt
dV/dt = 4/3 π[1-(0.9)^3](3r^3)(2)
dV/dt = 8(3.14)(0.271)(10)^3
dV/dt = 8(3.14)(0.271)(1000)
dV/dt = 681.097 cm^3/ week.
Hence, the volume of the rind is growing at the rate 681.097 cubic centimeters per week at the end of the fifth week.
To learn more about volume of the rind link is here
brainly.com/question/483402
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