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)

Thus, 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

Therefore, 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 × 22/7 × R² × h

V₁ = 1/3 × 22/7 × (2.5)² × 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 × 22/7 × 2.5² × 7.6 m²   = 49.67 m²      

Next,

Volume of the Cylindrical Portion (V₂) = πR²h

V₂ = 22/7 × 2.5² × 21 = 412.5 m²

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

V = 412.5 + 49.67 = 462.17 m²

Hence, the total volume of the Rocket is 462.17 m²