Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Join our platform to get reliable answers to your questions from a knowledgeable community of experts. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
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
#SPJ4
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.
