# Surface Area and Volume of A Right Circular Cylinder - Class 9 : Notes

(1) If r is the radius and h is the height of a right circular cylinder, then
(i) Curved (lateral) surface area =
For Example: If  radius $r = 5cm$ and height $h = 10cm$ , then
Curved (lateral) surface area $= 2\pi \times 5 \times 10 = 314c{m^2}$

(ii) Total surface area $= 2\pi r\left( {h + r} \right)$
For Example: If radius $r = 5cm$ and height $h = 10cm$ , then
Total surface area $= 2\pi \times 5\left( {10 + 5} \right) = 471c{m^2}$

(iii)  Volume $= \pi {r^2}h$
For Example: If radius $r = 5cm$ and height $h = 10cm$ , then
Volume $= \pi \times {5^2} \times 10 = 785c{m^3}$

(2) Let R and r be the external and internal radii of a hollow cylinder of height h. Then,
(i) Each base surface area $= \pi \left( {{R^2} - {r^2}} \right)$
For Example: If Internal radii $r = 5cm$ , external radii $R = 7cm$ and height $h = 10cm$, then
Each base surface area $= \pi \left( {{7^2} - {5^2}} \right) = 75.36c{m^2}$

(ii) Curved(lateral) surface area $= 2\pi rh\left( {R + r} \right)$
For Example: If Internal radii $r = 5cm$ , external radii $R = 7cm$ and height $h = 10cm$, then
Curved(lateral) surface area $= 2\pi \times 5 \times 10\left( {7 + 5} \right) = 3768c{m^2}$

(iii) Total surface area $= 2\pi \left( {R + r} \right)\left( {h + R - r} \right)$
For Example: If Internal radii $r = 5cm$ , external radii $R = 7cm$ and height $h = 10cm$, then
Total surface area $= 2\pi \left( {7 + 5} \right)\left( {10 + 7 - 5} \right) = 904.32c{m^2}$

(iv) Volume $= \pi \left( {{R^2} - {r^2}} \right)h$
For Example: If Internal radii $r = 5cm$ , external radii $R = 7cm$ and height $h = 10cm$, then
Volume $= \pi \left( {{7^2} - {5^2}} \right)10 = 753.6c{m^3}$