# Related rates: A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 2.6 ft/s.?

A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 2.6 ft/s.

(a) How rapidly is the area enclosed by the ripple increasing when the radius is 5 feet?

The area is increasing at _____ ft^2 /s.

(b) How rapidly is the area enclosed by the ripple increasing at the end of 8.2 seconds?

The area is increasing at _____ ft^2 /s.

### 3 Answers

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- Mike GLv 71 year agoFavourite answer
a) A = π(2.6t)^2 where t = time

A(t) = 6.76πt^2

A'(t) = 13.52πt

t = 5/2.6 = 1.923

A'(1.923) = 81.68 ft^2/s

b) A'(8.2) = 348.29 ft^2/s

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- Anonymous1 year ago
ㅤ

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- az_lenderLv 71 year ago
A = pi*r^2 =>

dA/dt = 2*pi*r dr/dt.

When r = 5,

dA/dt = 10*pi*(2.6) = 82 ft^2/s;

when t = 8.2 s, the r = (8.2 s)(2.6 ft/s) =>

dA/dt = 2*pi*8.2*2.6*2.6 = 348 ft^2/s.

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