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10 cards from this deck
Changes in one variable affect changes in another variable.
Identify the quantities that change with respect to time.
To differentiate equations related to changing quantities.
A=πr2A = \pi r^2A=πr2, where rrr is the radius of the circle.
dA/dt=2πr(dr/dt)dA/dt = 2\pi r(dr/dt)dA/dt=2πr(dr/dt), using implicit differentiation.
Volume V=(1/3)πr2hV = (1/3)\pi r^2 hV=(1/3)πr2h, with rrr in terms of hhh.
Indicates volume is decreasing over time.
dA/dt=20πdA/dt = 20\pidA/dt=20π cm²/s using A=πr2A=\pi r^2A=πr2 formula.
Ensure the solution is contextually sensible.
Geometry, motion problems, fluid dynamics, and engineering.
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