The ratio between the radius of the base and the height of a cylinder si `2 : 3`. If its volume is `1617 cm^(3)` then its total surface area is

Answer

`770 cm^(2)`

Explanation

Suppose that radius `= 2x cm` and height = 3x cm
Volume `= pir^(2) h = ((22)/(7) xx 4x^(2) xx 3x) = ((264x^(3))/(7)) cm^(3)`
`:. (264x^(3))/(7) = 1617 rArr x^(3) = ((1617 xx 7)/(264)) = ((7)/(2))^(3) rArr x = (7)/(2)`
Thus, r = 7 cm and h = 10.5 cm
Total surface area `= (2pi rh + 2pi r^(2)) = 2pi r(h + r)`