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Zielflug [23.3K]
2 years ago
14

The radius of the base of a cylinder is decreasing at a rate of 121212 kilometers per second. The height of the cylinder is fixe

d at 2.52.52, point, 5 kilometers. At a certain instant, the radius is 404040 kilometers. What is the rate of change of the volume of the cylinder at that instant (in cubic kilometers per second)
Mathematics
1 answer:
WARRIOR [948]2 years ago
4 0

Answer:

7536 km^3/sec

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.

Volume = \pi r^2h

Where r is the radius and

h is the height of cylinder.

As per question statement:

r = 40 km (variable)

h = 2.5 (constant)

\dfrac{dV}{dt} = \dfrac{d}{dt}\pi r^2h

As \pi, h are constant:

\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

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