# Right Circular Cylinder

Right Circular Cylinder

A cylinder whose base is a circle is called circular cylinder. If the axis of the cylinder is perpendicular to its base then the cylinder is called a right circular cylinder.

If $r$ is the radius of the circular base, $h$ is the height, $S$ is the lateral surface area, $V$ is the volume and $P$ is the perimeter of the base, then

$Volume\,of\,the\,cylinder\, = \,area\,of\,base\, \times \,height\,of\,cylinder$
i.e        (i)                     $V = \pi {r^2}h$     ($r$ being radius)
or         (ii)                    $V = \frac{\pi }{4}{d^2}h$          ($d$ being diameter)

Example:

Find the cost of digging a well 3m in diameter and 24m deep at the rate of Rs.10 per cu.m.

Solution:

Given that

Diameter of the well       $= 3m$
$\therefore$            Radius of the well,      $r = 1.5m$
Depth of the well,       $h = 24m$
$\therefore$            Volume of the earth excavated           $= \pi {r^2}h = \frac{{22}}{7} \times \left( {1.52} \right) \times 24$
$= 3.1416 \times 2.25 \times 24\,\,cu.\,m$
$= 169.646\,\,cu.\,m$
Now, cost per cu. m    $= {\text{Rs}}{\text{.}}\,10$
$\therefore$            ${\text{Total}}\,{\text{Cost}}\, = \,10 \times 169.646 = 1696.46\,{\text{rupees}}$

Example:

The volume of a cylindrical ring is 800 cu.cm. The radius of a cross section is 2cm. Find the length of the ring.

Solution:

Given that

Radius of cross section,          $r = 2\,{\text{cm}}$
Volume,                                  $v = 800\,{\text{cu}}{\text{.cm}}$

Let the length of the ring be   $h\,\,\,cm$
Now,   ${\text{Volume}}\, = \,{\text{area of cross – section }} \times {\text{ height}}$
$800\,\,\,\,\,\,\, = \pi {r^2} \times h$
$= \frac{{22}}{7} \times 4 \times h$

$\therefore$            $h = \frac{{800 \times 7}}{{22 \times 7}} = \frac{{700}}{{11}} = 63.6\,{\text{cm}}$