The radius of the base of a cylinder is decreasing at a rate of 12 kilometers per second. The height of the cylinder is fixed at 2.5, point, 5 kilometers. At a certain instant, the radius is 40 kilometers. What is the rate of change of the volume of the cylinder at that instant (in cubic kilometers per second)
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Ответ:
the rate of change of the volume of the cylinder at that instant is -2400π km³/s
Explanation:
Given that;
Height of cylinder h = 2.5 km
Radis r = 40 km
radius of the base of a cylinder is decreasing at a rate of 12 kilometers per second
that is; dr/dt = (-12) km/s
we know that; volume of a cylinder V = πr²h
now, we differentiate
dv/dt = π2r×dr/dt×h
so we substitute
dv/dt = 2π × 40 × (-12) × 2.5
dv/dt = -2400π km³/s
Therefore, the rate of change of the volume of the cylinder at that instant is -2400π km³/s
Ответ:
mutualism, parasitism
Explanation: