document.write( "Question 1170380: Air is blown into a Spherical balloon and the rate at which the volume is increasing is 3 ft^3 per minute. Find the rate at which the radius is increasing at the instant when the radius is 5 feet.\r
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Algebra.Com's Answer #795363 by math_helper(2461) $\"\"$ $\"About$

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Starting with the equation for the volume of a sphere:
\n" ); document.write( " $\"+V+=+%284%2F3%29pi%2Ar%5E3+\"$

\n" ); document.write( "you can relate the rate of change of volume WRT time (dV/dt) to the product (dV/dr)*(dr/dt):
\n" ); document.write( " $\"+dV%2Fdt+=+%28dV%2Fdr%29%2A%28dr%2Fdt%29+=+4pi%2Ar%5E2+%2A+%28dr%2Fdt%29+\"$ ... (1)
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\n" ); document.write( "\n" ); document.write( "Plugging into (1) the known values:
\n" ); document.write( " $\"+3+=+4pi%285%29%5E2+%2A+%28dr%2Fdt%29+\"$
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\n" ); document.write( "\n" ); document.write( "and solving for dr/dt:
\n" ); document.write( " $\"+dr%2Fdt+=+0.00955+\"$ ft/min \n" ); document.write( "

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