Answer:
7536 [tex]km^3/sec[/tex]
Step-by-step explanation:
Given that:
Rate of decreasing of radius = 12 km/sec
Height of cylinder is fixed at = 2.5 km
Radius of cylinder = 40 km
To find:
The rate of change of Volume of the cylinder?
Solution:
First of all, let us have a look at the formula for volume of a cylinder.
[tex]Volume = \pi r^2h[/tex]
Where [tex]r[/tex] is the radius and
[tex]h[/tex] is the height of cylinder.
As per question statement:
[tex]r[/tex] = 40 km (variable)
[tex]h[/tex] = 2.5 (constant)
[tex]\dfrac{dV}{dt} = \dfrac{d}{dt}\pi r^2h[/tex]
As [tex]\pi, h[/tex] are constant:
[tex]\dfrac{dV}{dt} = \pi h\dfrac{d}{dt} r^2\\\Rightarrow \dfrac{dV}{dt} = \pi h\times 2 r\dfrac{dr}{dt} \\$Putting the values:$\\\Rigghtarrow\dfrac{dV}{dt} = 3.14 \times 2.5\times 2 \times 40\times 12 \\\Rigghtarrow\dfrac{dV}{dt} = 7536\ km^3/sec[/tex]
