A rocket is in the form of a circular cylinder closed at the lower end and a cone of the same radius is attached to the top The radius of the cylinder is 2.5 m, its height is 21 m and the slant height of the cone is 8 m. Calculate the total surface area of the rocket.

Solution

Let r m be the radius, and h m be the height of the cylinder, then
r = 2.5 m and h = 21 m
Let r m be the radius and l m be the slant height of the cone, then
r₁ = 2.5 m and l = 8 m
Now,
The Total Surface Area of the rocket
= C.S.A of cone + C.S.A of cylinder + Area of base
= $straight pi$ r₁l + 2 $straight pi$ rh + $straight pi$ r²= $straight pi$ rl + 2 $straight pi$ rh + $straight pi$ r² [r₁ = r]
= $straight pi$ r (l + 2h + r)

$equals space open square brackets 22 over 7 straight x space 2.5 space left parenthesis 8 space plus 2 space straight x space 21 space plus space 2.5 close square brackets space straight m squared equals space open square brackets 22 over 7 straight x space 2.5 space straight x space 52.5 close square brackets space straight m squared equals space open parentheses fraction numerator 2887.5 over denominator 7 end fraction close parentheses straight m squared space equals space 412.5 space straight m squared$

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Statistics

A rocket is in the form of a circular cylinder closed at the lower end and a cone of the same radius is attached to the top The radius of the cylinder is 2.5 m, its height is 21 m and the slant height of the cone is 8 m. Calculate the total surface area of the rocket.

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