Question

The radius of a circular plate is increasing at the ratio of 0.20 cm/sec. At what rate is the area increasing when the radius of the plate is 25 cm.​

Answer 1

Answer:

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Now, differentiate the area relation with respect to time and substitute drdt=0.20cm/sec. Finally, substitute r = 25 cm in the obtained differential equation and get the value of dAdt. Hence, the rate of the increase of the area of the circular plate is 31.4cm2/sec.

Answer 2

Answer:

Given the radius of the circular plate is =r=25 cm.

Again rate of increase of radius = dt/dr =0.20 cm/sec.

The area of the circular plate =A= πr2cm2.

Now rate of increase in area of the plate is dt/ dA

=2πr dt/dr

=50×0.20π=10π cm2/sec