document.write( "Question 1125312: GENERAL: Hailstones A hailstone (a small sphere of ice) is forming in the clouds so that its radius is growing at the rate of 1 millimeter per minute. How fast is its volume growing at the moment when the radius is 2 millimeters? [Hint: The volume of a sphere of radius r is V = 4/3*pi r^3.] \n" ); document.write( "

Algebra.Com's Answer #741607 by ikleyn(52803) $\"\"$ $\"About$

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document.write( "You are given  V(t) = V(r(t)) = ,  where the radius  r  varies  such that   = 1 millimeter per minute.\r\n" );
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document.write( "Then   = . = . = 4*3.14*4 =  = 50.24 mm^3 per minute.\r\n" );
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document.write( "Thus the instantaneous volume growing rate is  50.24 mm^3/minute.\r\n" );
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document.write( "Interesting, that if you calculate the averaged volume growing rate between  t= 2 seconds  and  t= 3 seconds, you will get another value\r\n" );
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document.write( " =  -  =  =  =  = 79.55  mm^3/minute.\r\n" );
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document.write( "But it only demonstrates the difference between these two conceptions: instantaneous and averaged rates.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Answer. The instantaneous volume growing rate at this moment is 50.24 mm^3 per minute.\r
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