8th Class Mathematics Mensuration Surface Area and Volume of Cylinder

         Surface Area and Volume of Cylinder

            Surface Area of Cylinder

Total surface area of cylinder = curve surface area + 2 (area of face)

Total surface area \[=2\pi r(r+h)\]

Curve surface area \[=2\pi rh\]  

            Volume of Cylinder

Volume of cylinder \[=\pi {{r}^{2}}h\]

Where r is the radius of cylinder and h is the height of cylinder.  

            Surface Area of Cone

A cone is a solid with a circular base. It has a curved surface which tapers (i.e. decreases in size) towards the vertex along the top.

The height of the cone is the perpendicular distance from the base to the vertex.   

Now, \[\frac{Area\,of\,\sec tor\,ABC}{Area\,of\,circle\,with\,centre\,at\,C}=\] \[\frac{Arc\,length\,AB\,of\sec tor\,ABC}{Circumference\,of\,circle\,with\,centre\,at\,C}\]

Area of sector ABC \[=\frac{r}{l}\times \pi {{l}^{2}}=\pi rl\].

The curved surface area of a cone = The area of sector ABC.

\[\therefore \] The curved surface area of a cone\[=\pi rl\]

Total surface area of the cone = Area of the base + Curved surface area

\[\therefore \] \[TSA=\pi {{r}^{2}}+\pi rl\]

or, \[TSA=\pi r(r+l)\].

The volume of the cone is given by,

\[V=\frac{1}{3}\pi {{r}^{2}}h\]