Question

2004)
12. 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.​

Answer 1

$\huge \tt \colorbox{pink}{Solution}$

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Given ,

Radius of the cylindrical portion of the rocket (R) = 2.5m

Height of the cylindrical portion of the rocket (H) = 21m

Slant height of the conical surface of the rocket (L) = 8m

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Curved Surface Area of the cone (S1) = πRL = π (2.5)(8) = 20 π

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And,

Curved Surface Area of the cylinder (S2)

$\tt \ = 2πRH + π { R}^{2}$

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$\tt \: S _{2 } \: = (2\pi \times 2.5 \times 21) + \pi {2.5}^{2}$

$\tt \: = > S_{2} = (\pi \times 105) + (\pi \times 6.25)$

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Thus , The total Curved Surface Area S is

S = S1 + S2

S = (π20) + (π6.25)

$\tt \: S = ( \frac{22}{7} )(20 + 105 + 6.25)$

$\tt S \: = \frac{22}{7} \times 131.25$

$\tt \red{ \: S = 412.5 \: {m}^{2} }$

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Therefore, the total Surface Area of the Conical Surface = 412.5 m^2

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