Question

A wooden toy rocket is in the shape of a cone mounted on a cylinder, as shown in Fig. The height of the entire rocket is 26 cm, while the height of the conical part is 6 cm. The base of the conical portion has a diameter of 5 cm, while the base diameter of the cylindrical portion is 3 cm. 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 colours. (Take $\pi =3.14$) [4 MARKS]

Answer 1

Concept: 1 Mark
Application: 3 Marks

Denote radius of cone by r, slant height of cone by $l$, height of cone by h, radius of cylinder by r' and height of cylinder by h'.

Then r = 2.5 cm, h =6 cm, r'= 1.5cm,

h'= 26 - 6 = 20 cm and

$l=\sqrt{r^2+h^2}=\sqrt{{2.5}^2+6^2}cm=6.5cm$

Here, the conical portion has its circular base resting on the base of the cylinder, but

the base of the cone is larger than the base of the cylinder. So, a part of the base of the cone (a ring) is to be painted.

So, the area to be painted orange = CSA of the cone + base area of the cone - base area of the cylinder

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

$=\pi \left[\right(2.5\times 6.5)+(2.5{)}^2-\left(1.5{)}^2\right]c{m}^2$

$=\pi \left[20.25\right]c{m}^2=3.14\times 20.25c{m}^2$

$=63.585c{m}^2$,

Now, the area to be painted yellow = CSA of the cylinder + area of one base of the cylinder

$=2\pi r^{{}^{\prime }}{h}^{{}^{\prime }}+\pi (r^{\prime }{)}^2$

$=\pi r^{\prime }(2h^{\prime }+r^{\prime })$

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

$=4.17\times 41.5c{m}^2$

$=195.465c{m}^2$