Chapter ISG, Problem 9.6.3P

To determine

To find radius of circle.

Answer to Problem 9.6.3P

radius is 8 cm

Explanation of Solution

Given information:

Cylinder

Base radius is x

Height is 8 cm

E removed $40x$ $c{m}^3$

Remain volume 250 $c{m}^3$

Formula used:

Volume of cylinder, $=\frac{1}{3}\pi r^{2}h$

  $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Calculation:

Using formula

  $\frac{1}{3}\pi r^{2}h=250+40x$

Put value of radius and height

  $\frac{1}{3}\pi x^2(8)=250+40x$

On solving,

  $\pi x^2(8)=750+120x$

On solving,

  $4\pi x^2-60x-350=0$

On solving,

  $a=4\pi$

  $b=-60$

  $c=-375$

Using quadratic formula

  $x=\frac{-(-60)\pm \sqrt{{(-60)}^2-4(4\pi )(-375)}}{2(4\pi )}$

On solving,

  $x=\frac{60\pm \sqrt{3600+6000\pi )}}{8\pi }$

On solving,

  $x_1=\frac{60+\sqrt{3600+6000\pi )}}{8\pi }$

  $x_2=\frac{60-\sqrt{3600+6000\pi )}}{8\pi }$

On solving,

  $x_1\approx -3.57$ and $x_2\approx 8.34$

Hence, approximate radius is 8 cm