#### 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 2.5m and height 21m and the cone has a slant height 8m. Calculate total surface area and volume of the rocket?

#### Solution

Given radius of cylinder (a) = 2.5m

Height of cylinder (h) = 21m

Slant height of cylinder (l) = 8m

Curved surface area of cone(S_{1}) = πrl

S_{1} = π(2.5)(8)cm^{2} ...........(1)

Curbed surface area of a cone`= 2pirh+pir^2`

`S_2=2pi(2.5)(21)+pi(2.5)^2cm^2` ...........(2)

∴Total curved surface area = (1) + (2)

S = S_{1} + S_{2}

S = π(2.5)(8) + 2π(2.5)(21) + π(2.5)^{2}

S = 62.831 + 329.86 + 19.63

S = 412.3m^{2}

∴Total curved surface area = 412.3m^{2}

Volume of a cone `=1/3pir^2h`

`V_1=1/3xxpi(2.5)^2h cm^3` .........(3)

Let ‘h’ be height of cone

`l^2=r^2+h^2`

⇒ `l^2-r^2=h^2`

⇒ `h=sqrt(l^2-r^2)`

⇒ `h=sqrt(8^2-25^2)`

⇒ h =23.685m

Subtracting ‘h’ value in(3)

Volume of a cone `(V_1)=1/3xxpi(2.5)^2(23.685) cm^2` ........(4)

Volume of a cylinder `(V_2)=pir^2h`

`=pi(2.5)^2 21m^3` ...........(5)

Total volume = (4) + (5)

V = V_{1} + V_{2}

⇒ `V=1/3xxpi(2.5)^2(23.685)+pi(2.5)^2=1`

⇒ V = 461.84m^{2}

Total volume (V) = 461.84m^{2}