Chapter 9.2, Problem 55E

To determine

To calculate approximate radius of the cylinder

Answer to Problem 55E

  $r=4ft$

Explanation of Solution

Given information:

Height( h ) of the cylinder is 6 feet

Surface area of cylinder is $225f{t}^2$

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

  $225=2\pi r(r+6)$

On solving

  $112.5=\pi r(r+6)$

On solving

  $\frac{112.5}{\pi }=r(r+6)$

On solving

  $\frac{112.5}{3.14}=r(r+6)$

On solving

  $\frac{112.5}{3.14}=r(r+6)$

On solving

  $35.8280=r(r+6)$

On solving

  $35.8280=r(r+6)$

On solving

  $35.8280=r^2+6r$

On solving

  $\frac{8957}{250}=r^2+6r$

On solving

  $8957=250r^2+1500r$

On solving

  $r=\frac{-1500\pm \sqrt{{1500}^2-4\times 250\times (-8957)}}{2\times 250}$

On solving

  $r=\frac{-1500\pm \sqrt{{1500}^2+8957000}}{500}$

On solving

  $r=\frac{-1500\pm \sqrt{{10}^2\times ({150}^2+89570)}}{500}$

On solving

  $r=\frac{-1500\pm \sqrt{{10}^2\times (22500+89570)}}{500}$

On solving

  $r=\frac{-1500\pm 10\sqrt{112070}}{500}$

Simplify the expressions

  $r=\frac{-1500+10\sqrt{112070}}{500}$

  $r=\frac{-1500-10\sqrt{112070}}{500}$

Simplify the expressions

  $r=\frac{-150+\sqrt{112070}}{50}$

  $r=\frac{-150-\sqrt{112070}}{50}$

Simplify the expressions

  $r\approx 3.69$

  $r=-9.69$

Radius cannot be negative

Hence, approximate answer is $r=4ft$