When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.01 cm divided by min. At what rate is the plate's area increasing when the radius is 41 cm?

2.56cm2/min

Explanation: From the knowledge of deferential calculus,

Let r = radius (in cm) at time t min

A = area (in cm2) at time t min

A = πr2

GIVEN: dr/dt = 0.01cm/min

FIND: dA/dt when r =41 cm

Differentiate the area formula with respect to t:

dA/dt = π(2r)(dr/dt)

= π(2(41cm))(0.01cm/min)

= 82π × 0.01cm2/min

= 3.142 ×82×0.01

= 2.56cm2/min

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