Question

A wooden toy rocket is in the shape of a cone mounted on a cylinder, as show in fig:13.8. 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 cm, while the base diameter of the cylindercal 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 colour $\left(\text{take}\pi =3.14\right)$

Answer 1

Area to be painted orange $=$

Conical Area $=\pi L_1\frac{d_1}{2}+\frac{\pi }{4}(d_1^2-d_2^2)$

$\to L_1=\sqrt{6^2+{2.5}^2}=6.5$

Orange Area $=\pi \times 6.5\times \frac{5}{2}+\frac{\pi }{4}(25-9)$

$=\pi (16.25-4)$

$=12.25\pi c{m}^2$

$=38.465c{m}^3$

Yellow Area $=$ Cylinderical Area $=\frac{\pi d_2^2}{4}+2\pi \frac{d_2}{2}\times h_2$

$=\pi \frac{9}{4}+\pi \times 3\times 20$

$=2.25\pi +60\pi$

$=195.465c{m}^2$