Question

A wooden toy rocket is in the shape of a cone mounted on a cylinder as shown in figure. The height of the entire rocket is $26cm$, while the height of the conical part is $6cm$. The base of the conical portion has a diameter of $5cm$, while the base diameter of the cylindrical portion is $3cm$. If the conical portion is to be painted orange and the cylindrical portion yellow, find the area of the rocket painted with each of these coloures . (Take $\pi =22/7$)

Answer 1

Let $r$ be the radius of the base of the cone and its slant height be $l$. Further, let $r_1$ be the radius of the cylinder and $h_1$ be its height

We have
$r=2.5cm,h=6cm$
$r_1=1.5cm;h_1=20cm$

Now $l=\sqrt{r^2+h^2}\Rightarrow l=\sqrt{{\left(2.5\right)}^2+6^2}=6.5cm=\sqrt{4.25+36}=\sqrt{40.25}$

Now
area to be painted orange = curved surface area of the cone + base area of the cone - base area of the cylinder

$\Rightarrow \pi rl+\pi r^2-\pi r_1^2$

$=\pi \{rl+r^2-r_1^2\}$

$=\pi \{2.5\times 6.6+{\left(2.5\right)}^2-{\left(1.5\right)}^2\}{cm}^2$

$=3.14(16.25+6.25-2.25){cm}^2=63.585{cm}^2$

Area to be painted yellow

$=$ curved surface area of the cylinder + area of the base of the cylinder

$=2\pi r_1{h}_1+\pi r_1^2$

$=\pi r_1(2h_1+r_1)$

$=3.14\times 1.5(2\times 20+1.5){cm}^2$

$=195.465{cm}^2$