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.


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}}