Chapter 9.2, Problem 56E

To determine

To calculate approximate radius of the cylinder

Answer to Problem 56E

  $r\approx 6ft$

Explanation of Solution

Given information:

Height( h ) of the cylinder is 13 feet

Surface area of cylinder is $750f{t}^2$

Formula used:

Surface area of a cylinder( S )

  $=2\pi r(r+h)$

Calculation:

Substituting the value of Surface area of a cylinder( S ) and height( h ) in the formula

  $750=2\pi r(r+13)$

On solving

  $375=\pi r(r+13)$

On solving

  $\frac{375}{\pi }=r(r+13)$

On solving

  $\frac{375}{3.14}=r(r+13)$

On solving

  $119.4267=r(r+13)$

On solving

  $\frac{1194267}{10000}=r^2+13r$

On solving

  $1194267=10000r^2+130000r$

On solving

  $-10000r^2-130000r+1194267=0$

On solving

  $r=\frac{-130000\pm \sqrt{{130000}^2-4\times 10000\times (-119467)}}{2\times 10000}$

On solving

  $r=\frac{-130000\pm \sqrt{{130000}^2+47770680000}}{20000}$

Simplify the expressions

  $r=\frac{-130000+\sqrt{{130000}^2+47770680000}}{20000}$

  $r=\frac{-130000-\sqrt{{130000}^2+47770680000}}{20000}$

Simplify the expressions

  $r\approx 6.21$

  $r=-19.21$

Radius cannot be negative

Hence, approximate answer is $r\approx 6ft$