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Dividing both sides by $\pi$, $16x^2+12x+ 1= 182$Subtracting 182 from both sides, $16x^2+ 12x- 181= 0$This quadratic equation can be solved to find the value of $x$. Once $x$ is found, we can determine the diameter of the cylinder by substituting it into the expression $4x+2$. In summary, we can determine the diameter of a cylinder with a given surface area of $182\pi$ by solving the quadratic equation $16x^2+

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- #2

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from the sketch, $r = \dfrac{4x+2}{2}$ and $h=2x$

substitute for $r$ and $h$ and set equal to $182\pi$, solve for $x$, then determine the diameter

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Dividing both sides by $\pi$, $16x^2+12x+ 1= 182$. Subtracting 182 from both sides, $16x^2+ 12x- 181= 0$. Solve that quadratic equation for x.

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$2\pi (2x+1)^2 + \pi(8x^3+4x) = \pi(8x^2+8x + {\color{red}2} +8x^2+4x)$

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