A solid cylinder has total surface area of 462 cm^2. its curved surface area is one - third of its total surface area . Find the volume of the cylinder .

Answers (1)

Solution :  Let r be the radius of  the base and h be the height of the cylinder . Then, 

                 Total surface area = 2pi r(h+r)cm^2   ,   Curved surface area = 2pi rh cm^2

We have , 

                Curved surface area = frac13 (Total surface area) = frac13	imes 462 cm^2

Rightarrow                                               2pi rh=154cm^2   .....................(1)

        Again,       Total surface area = 462cm^2

Rightarrow                     2pi rh +2pi r^2=462

Rightarrow                     154+2 pi r^2 =462

Rightarrow                     2	imes frac227	imes r^2= 462-154Rightarrow r^2=49Rightarrow r=7cm

From (1) , We have 

                                2	imes frac227	imes 7 	imes h=154Rightarrow h=frac72 cm

Hence , Volume of the cylinder     

                                                =pi r^2h=frac227	imes7^2 	imes frac72cm^3= 539 cm^3

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