Answer:
726.34 cm/min
Step-by-step explanation:
Volume of a sphere:
The volume of a sphere is given by the following equation:
[tex]V = \frac{4\pi r^3}{3}[/tex]
In which r is the radius.
Implicit derivatives:
This question is solving by implicit derivatives. We derivate V and r, implicitly as function of t. So
[tex]\frac{dV}{dt} = 4\pi r^2 \frac{dr}{dt}[/tex]
A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.2 cm/min.
This means that [tex]\frac{dr}{dt} = -0.2[/tex]
At what rate is the volume of the snowball decreasing when the radius is 17 cm.
This is [tex]\frac{dV}{dt}[/tex] when [tex]r = 17[/tex]
[tex]\frac{dV}{dt} = 4\pi r^2 \frac{dr}{dt}[/tex]
[tex]\frac{dV}{dt} = 4\pi*(17)^2*(-0.2)[/tex]
[tex]\frac{dV}{dt} = -726.34[/tex]
This means that the volume of the snowball is decreasing at a rate of 726.34 cm/min when the radius is 17 cm.
