Question 1104057
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Given that the height is 8, the total surface area is {{{2(pi)r^2+2(pi)rh = 2(pi)r^2+16(pi)r}}}<br>
Given that the total surface area is 40pi,<br>
{{{2(pi)r^2+16(pi)r = 40pi}}}
{{{2(pi)r^2+16(pi)r-40(pi) = 0}}}
{{{r^2+8r-20 = 0}}}  [dividing out the common factor 2pi]
{{{(r+10)(r-2) = 0}}}<br>
r = -10 or r=2; since this is the radius of the cylinder, we reject the negative solution.<br>
The radius of the cylinder is 2.