A rocket is in the form of a right circular cylinder closed at the lower end and surmounted by a cone with the same radius as that of the cylinder. The diameter and height of the cylinder are 6 cm and 12 cm, respectively. If the slant height of the conical portion is 5 cm, then find the total surface area and volume of the rocket. 
The diagram is given as:
For upper conical part,
Radius of base, r = 3 cm
Slant height, l = 5 cm
As,
l2 = h2 + r2, where h , r and l are height radius respectively.
h2 = l2 - r2
⇒ h2 = (5)2 - (3)2
h2= 25 - 9 = 16
h = 4 cm
Also,
volume of cone
Curved surface area of cone = πrl = π(3)(5) = 15π cm2
For cylindrical part,
Radius of base = Radius of base of conical part = r = 3 cm
Height, h = 12 cm
Also,
Volume of cylinder = πr2h = π(3)2(12) = 108π cm3
Curved surface area of cylinder = 2πrh = 2π(3)(12) = 72π cm2
Volume of rocket = volume of conical part + volume of cylindrical part
Volume of rocket = 12π + 108π = 120π
Also,
Surface area of rocket = Curved surface area of conical part + Curved surface area of Cylindrical part + Surface area of base of rocket
Surface area of base of rocket = πr2 = π(3)2 = 9π cm2
Therefore,
Surface area of rocket = 15π + 72π + 9π = 94π cm2
