document.write( "Question 694379: The total surface area of a can is 384pi square inches. Find the dimensions of the can if the volume is a maximum. \n" ); document.write( "

Algebra.Com's Answer #427850 by htmentor(1343) $\"\"$ $\"About$

You can put this solution on YOUR website!
V = pi*r^2*L
\n" ); document.write( "Surface area, S = 2*pi*r*L + 2*pi*r^2 = 384*pi
\n" ); document.write( "First you would solve for L in terms of r.
\n" ); document.write( "Doing the algebra you will get L = 192/r - r
\n" ); document.write( "The volume will be maximum where dV/dr = 0
\n" ); document.write( "Taking the derivative and carrying out the algebra you will get the expression
\n" ); document.write( "3r^2 = 192 -> r = 8
\n" ); document.write( "Therefore L = 192/8 - 8 = 16
\n" ); document.write( "Ans: length 16 in., radius 8 in.
\n" ); document.write( "We can see that the answer is correct by plotting V as a function of r
\n" ); document.write( "V=pi*r^2*(192/r - r); r along the x-axis:
\n" ); document.write( " $\"graph%28300%2C300%2C-2%2C20%2C-200%2C3500%2Cpi%2Ax%5E2%2A%28%28192%2Fx%29-x%29%29\"$
\n" ); document.write( " \n" ); document.write( "

\n" );