A cylinder of radius r cm and height h cm has a curved surface area A cm². Where –
a) We are asked to find formula for h.
[tex]\qquad[/tex][tex]\purple{ \bf \longrightarrow A=2 \pi rh }[/tex]
First, overturn the equation
[tex]\qquad[/tex][tex] \sf \longrightarrow 2 \pi rh =A[/tex]
Divide both sides by 2πr
[tex]\qquad[/tex][tex] \sf \longrightarrow \dfrac{2\pi rh}{2\pi r } = \dfrac{A}{2\pi r}[/tex]
[tex]\qquad[/tex][tex] \sf \longrightarrow \dfrac{\cancel{2 \pi r }h}{\cancel{2\pi r} } = \dfrac{A}{2\pi r}[/tex]
[tex]\qquad[/tex][tex] \purple{\bf \longrightarrow h = \dfrac{A}{2 \pi r }}[/tex]
b) Again, we are given –
- Curved surface area, A = 93 cm²
- Radius, r = 2.5 cm
- π = 3.1
[tex]\qquad\qquad\quad\underline{\sf{Substituting \ Values \ :}}[/tex]
⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━
[tex]\qquad[/tex][tex] \bf \longrightarrow h = \dfrac{A}{2\pi r }[/tex]
[tex]\qquad[/tex][tex] \sf \longrightarrow h = \dfrac{93}{2 \times 3.1 \times 2.5 }[/tex]
[tex]\qquad[/tex][tex] \sf \longrightarrow h = \dfrac{93}{15.5}[/tex]
[tex]\qquad[/tex][tex] \sf \longrightarrow h =\cancel{ \dfrac{93}{15.5}}[/tex]
[tex]\qquad[/tex][tex]\pink{ \bf \longrightarrow h = 6\: cm }[/tex]
- Henceforth, height of the cylinder is 6 cm.
