. A rocket is in the form of a right circular cylinder


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 cylinder. The diameter and height of cylinder are 6cm and 12cm, respectively. If the slant height of the conical portion is 5cm, then find the total surface area and volume of rocket. (Use = 3.14 )

 

Best Answer

Explanation:

Given, 

Diameter = 6 cm

Radius (R) = 6/2 = 3cm

Height (H) = 12cm

Cylinder: Slant height (l) = 5cm

Radius (r) = 3cm

⇒ Height (h) = √l2-r2 [∴ l2=r2+h2]

h = 4cm

Now, volume of rocket = volume of cylinder + volume of cone

= πR2H + 1/3 πr2h

= πr2(H+1/3 h)

= 3.15 × 3 × 3 × [12 + 1/3 × 4] cm3

= 376.8 cm3

Also,

Total surface area of rocket = Curved surface area of cylinder + Curved surface area of cone + Area of area of base of cylinder

= 2πRH + πrl + πr2 (R = r = 3cm)

= πr[2H + l + r]

= 3.14 × 3[2 × 12 + 5 + 3]

= 301.44cm2

Final Answer:

Hence, the total surface area and volume of the rocket are 301.44 cm2, 376.8cm2 respectively.

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