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Question -

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



Answer -

Given,

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

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

Slant Height of theConical surface of the rocket (L) = 8 m

Curved Surface Area ofthe Cone (S1) = πRL = π(2.5)(8)= 20π

And,

Curved Surface Area ofthe Cone (S2) = 2πRH + πR2

S=(2π × 2.5 × 21) + π (2.5)2

S2 =(π × 105) + (π × 6.25)

Thus, the total curvedsurface area S is

S = S1 +S2

S = (π20) + (π105) +(π6.25)

S = (22/7)(20 + 105 +6.25) = 22/7 x 131.25

S = 412.5 m2

Therefore, the totalSurface Area of the Conical Surface = 412.5 m2

Now, calculating thevolume of the rocket

Volume of the conicalpart of the rocket (V1) = 1/3 × 22/7 × R2 × h

V1 = 1/3× 22/7 × (2.5)2 × h

Let, h be the heightof the conical portion in the rocket.

We know that,

L2 = R+h2

h2 = L–R2 = 82 – 2.52

h = 7.6 m

Using the value of h,we will get

Volume of the conicalpart (V1) = 1/3 × 22/7 × 2.52 × 7.6 m2   =49.67 m2      

Next,

Volume of theCylindrical Portion (V2) = πR2h

V2 = 22/7× 2.52 × 21 = 412.5 m2

Thus, the total volumeof the rocket = V1 + V2

V = 412.5 + 49.67 =462.17 m2

Hence, the totalvolume of the Rocket is 462.17 m

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