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 1

Curved surface area of cone $=\pi rl=\frac{22}{7}\times 2.5\times 8=62.85m^2$

Curved surface area of cylinder $=2\pi rh=2\times \frac{22}{7}\times 2.5\times 21=330m^2$

Area of the base circle of the cylinder $=\pi r^2=\frac{22}{7}\times 2.5\times 2.5=19.64m^2$

Hence, total surface area of rocket$=62.85+330+19.64=412.5m^2$

Now, volume of cylinder $=\pi r^{2}h=\frac{22}{7}\times 2.5\times 2.5\times 21=412.5m^3$

For the cone, $l^2={h^{\prime }}^2+r^2$

$\Rightarrow 8^2={h^{\prime }}^2+{2.5}^2$

$\Rightarrow h^{\prime }=7.59m$

Volume of the cone $=\frac{1}{3}\pi r^2{h}^{\prime }=\frac{1}{3}\times \frac{22}{7}\times 2.5\times 2.5\times 7.59=49.69m^3$

Hence, total volume of rocket $=412.5+49.69=462.19m^3$