Cylinder: Formulas of Surface Areas and Volume

Cylinder

For a Cylinder of radius r and height h

(i) Total surface area = $2\pi r(h+r)$

(ii) Lateral(curved) surface area = $2\pi rh$

(iii) Base area of cylinder = $\pi {{r}^{2}}$

(iv) Volume of cylinder = $\pi {{r}^{2}}h$

Hollow Cylinder

Solids like iron pipes, rubber tubes are hollow cylinders.

Let R and r be the external and internal radii of a hollow cylinder and h be its height.

(i) Total surface area
                                $\begin{align}
                                & =2\pi Rh+2\pi rh+2\pi ({{R}^{2}}-{{r}^{2}}) \\
                                & =2\pi h(R+r)+2\pi (R+r)(R-r) \\
                                & =2\pi (R+r)(h+R-r) \\
                             \end{align}$ 
  
(ii) Lateral(curved) surface area = (External surface area) + (internal surface area)
                                                 = $2\pi Rh+2\pi rh=2\pi h(R+r)$ 
  
(iii) Base surface area = $\pi ({{R}^{2}}-{{r}^{2}})$ 
  
(iv) Volume of the material = Exterior volume – Interior volume
                                          = $\pi {{R}^{2}}h-\pi {{r}^{2}}h=\pi ({{R}^{2}}-{{r}^{2}})h$


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