Math CentralQuandaries & Queries


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.


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