Chapter 12.3, Problem 26WE

To determine

To calculate: The value of r

Answer to Problem 26WE

The value of r is $r=3$ units

Explanation of Solution

Given information: Consider the given information,

Total area of a cylinder = $90\pi$

Height of cylinder = 12units

Formula used: Consider the given formula,

r = radius, h = height

  $TA=2\pi rh+2\pi r^2$

Calculation : The solution for the following equation is,

  $90\pi =2\pi (12r+r^2)$

  $45=12r+r^2$

  $r^2+8r-45=0$

  $r^2+15r-3r-45=0$

  $r(r+15)-3(r+15)=0$

  $(r+15)(r-3)=0$

  $r+15=0$ and $r-3=0$

  $r=-15$ (not possible)

  $r=3$ units

Therefore, the value of is $r=3$ units