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 Question from Jazmin, a student: Hi, I don't understand how to find the radius in a cylinder with only the surface area (143.7) and the height (0.8)? I know that the formula is 2pir2+2pirh, but I don't see how to isolate the r? I appreciate your help.

Hi Jazmin,

Substituting the known values into the expression you have for the surface area gives

$2 \pi r^2 + 2 \pi r \times 0.8 = 143.7.$

Taking out a common factor of $2 \pi$ gives

$2 \pi \left(r^2 + 0.8 r \right) = 143.7.$

Divide both sides by $2 \pi$ and then transfer the constant to the left side of the equation to yield a quadratic equation of the form

$a r^2 + br + c = 0.$

Use the general quadratic formula to solve for $r.$ You should obtain two values for $r$ but you know that $r$ must be positive.

Penny

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