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