Q:

the total surface area of a solid cylinder is 21cm if the curved surface area of the solid cylinder is two - third of its total surface area find its radius and height​

Accepted Solution

A:
Answer:The radius of cylinder is 1.05 cm and The height of cylinder is 2.11 cmStep-by-step explanation:Given as :The total surface area of cylinder = 21 cmThe curved surface area of cylinder = [tex]\frac{2}{3}[/tex] of the total surface areaI.e The curved surface area of cylinder = [tex]\frac{2}{3}[/tex] × 21 = 14 cm∵ The total surface area of cylinder = 2 [tex]\pi[/tex] r h + 2 [tex]\pi[/tex] r² Where r is the radius and h is the height of cylinderOr, 2 [tex]\pi[/tex] r h + 2 [tex]\pi[/tex] r² = 21 cmOr,  [tex](2\times \Pi \times r\times h) + (2\times \Pi\times r^{2} )[/tex] = 21 cm   ....aAgain ∵ The curved surface area of cylinder = 2 [tex]\pi[/tex] r hWhere r is the radius and h is the height of cylinderOr, 2 [tex]\pi[/tex] r h = 14 cm    . ...bso . put the value of a into bI.e 14 cm + [tex](2\times \Pi\times r^{2} )[/tex] = 21 cm   Or,  [tex](2\times \Pi\times r^{2} )[/tex] = 21 cm - 14 cmOr, [tex](2\times \Pi\times r^{2} )[/tex] = 7so , r² = [tex]\frac{7}{2\pi }[/tex]∴    r² =  [tex]\frac{49}{44}[/tex]I.e  r = [tex]\sqrt{\frac{49}{44} }[/tex]So, radius = [tex]\frac{7}{\sqrt{44} }[/tex]  cmor,   r = 1.05 cmPut the value of r in eq b 2 [tex]\pi[/tex] r h = 14 cm Or,  2 [tex]\pi[/tex] ×  [tex]\frac{7}{\sqrt{44} }[/tex]  × h = 14 cmSo, h = [tex]\frac{\sqrt{44} }{\pi }[/tex]Or, h = 2.11 cmHence The radius of cylinder is 1.05 cm and The height of cylinder is 2.11 cm  Answer