Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Experience the convenience of getting reliable answers to your questions from a vast network of knowledgeable experts. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
Using implicit differentiation, it is found that the radius is increasing at a rate of 0.0081 cm per minute.
What is the volume of a sphere?
The volume of a sphere of radius r is given by:
[tex]V = \frac{4\pi r^3}{3}[/tex]
Applying implicit differentiation, the rate of change is given by:
[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]
In this problem, we have that:
[tex]\frac{dV}{dt} = 500, r = 70[/tex]
Hence the rate of change of the radius is given as follows:
[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]
[tex]19600\pi\frac{dr}{dt} = 500[/tex]
[tex]\frac{dr}{dt} = \frac{500}{19600\pi}[/tex]
[tex]\frac{dr}{dt} = 0.0081[/tex]
The radius is increasing at a rate of 0.0081 cm per minute.
More can be learned about implicit differentiation at https://brainly.com/question/25608353
#SPJ1
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.
