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A stone is dropped into a quiet lake and waves move in circles

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A stone is dropped into a quiet lake and waves move in circles at a speed of 4cm per second. At the instant, when the radius of the circular wave is 10 cm, how fast is the enclosed area increasing?

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A stone is dropped into a quiet lake and waves move in circles at a speed of 4cm per second. At the instant, when the radius of the circular wave is 10 cm, how fast is the enclosed area increasing?

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Text solutionVerified

Solution: given that,

\frac{d r}{d t} = 4

cm/s

r = 10

cm

A = π r^{2}

\frac{d A}{d t} = \frac{d π r ^{2}}{d t} = π \frac{d r ^{2}}{d t}

= π \frac{d r ^{2}}{d r} \frac{d r}{d t}

= π (2 r) (4)

= 2 π 10 \cdot 4 c m^{2}

/s

= 80 π c m^{2}

/sec
answer

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Question Text	A stone is dropped into a quiet lake and waves move in circles at a speed of 4cm per second. At the instant, when the radius of the circular wave is 10 cm, how fast is the enclosed area increasing?
Answer Type	Text solution:1
Upvotes	150