Question

The ratio of carved surface are to the total surface area if a right circular cylinder is 1:3 find the volume of the cylinder of its total surface area is1848

Answer 1

Let r is the radius and h is the height of the cylinder.

So  curved surface area (CSA) = 2*Π*r*h

Total surface area (TSA) = 2*Π*r*(h + r)

Now from question 

      CSA/TSA = 1/3

=> {2*Π*r*h}/{2*Π*r*(h + r)} = 1/3

=> h/(h+r) = 1/3

=> 3h = h + r

=> 3h - h = r

=> 2h = r

Again given

TSA = 1848

=> 2*Π*r*(h + r)} = 1848

=> 2*Π*2h(h+2h) = 1848

=> 2*Π*2h*3h = 1848

=> 12*Π*h2 = 1848

=> h2 = 1848/12Π

=> h2 = (1848*7)(12*22)

=> h2 = (84*7)12                (1848 and 22 are divided by 22)

=> h2 = 7*7                         (84 and 12 are divided by 12)

=> h2 = 49

=> h = √49

=> h = 7

Now volume of cylinder = Π*r2 *h

                                     =Π*(2h)2 *h

                                     =4Π*h3

                                     =(4*22*73 )/7

                                     = 4*22*49

                                     = 4312

So volume of the cylinder is 4312 cm3