# 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 Rate this question :

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