document.write( "Question 1060474: A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 2ft/s. How rapidly is the area enclosed by the ripple increasing at the end of 13s? \n" ); document.write( "
Algebra.Com's Answer #675415 by rothauserc(4718)\"\" \"About 
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we use the formula for the area of a circle and use the implicit derivative
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\n" ); document.write( "A = pi * r^2, where A is the area, r is the radius and pi = 22/7
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\n" ); document.write( "we now take the implicit derivative with respect to time
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\n" ); document.write( "dA/dt = 2 * pi * r * (dr/dt)
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\n" ); document.write( "we are given that (dr/dt) = 2 and asked to evaluate the Area's rate of change after 13 seconds
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\n" ); document.write( "we use the circumference of the circle to get r after 13 seconds
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\n" ); document.write( "C = 2 * pi * r, where C is the circumference, then
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\n" ); document.write( "dC/dt = 2 * pi * (dr/dt) = 2 * pi * 2 = 4 * pi per second
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\n" ); document.write( "after 13 seconds C = 4 * pi * 13 = 52 * pi
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\n" ); document.write( "52 * pi = 2 * pi * r
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\n" ); document.write( "r = 26
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\n" ); document.write( "dA/dt = 2 * pi * 26 * 2 = 326.7256 square feet / second
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