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.

Given,

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

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

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

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

And,

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

S2 = (2π × 2.5 × 21) + π (2.5)2

S2 = (π × 105) + (π × 6.25)

Hence, the total curved surface 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

Hence, the total Surface Area of the Conical Surface = 412.5 m2

Now, calculating the volume of the rocket

Volume of the conical part of the rocket (V1) = 1/3 x 22/7 x R2 x h

V1 = 1/3 x 22/7 x (2.5)2 x h

Let, h be the height of the conical portion in the rocket.

We know that,

L2 = R2 + h2

h2 = L2 – R2 = 82 – 2.52

h = 7.6 m

Using the value of h, we will get

Volume of the conical part (V1) = 1/3 x 22/7 x 2.52 x 7.6 m2 = 49.67 m2

Volume of the Cylindrical Portion (V2) = πR2h

V2 = 22/7 x 2.52 x 21 = 412.5 m2

Hence, the total volume of the rocket = V1 + V2

V = 412.5 + 49.67 = 462.17 m2

Therefore, the total volume of the Rocket is 462.17 m2

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