Question

A wooden toy rocket is in the shape of a cone mounted on a cylinder, as shown 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 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 π= 3.14)

Answer 1

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'= 1.5 cm, h'= 26 – 6 = 20 cm and

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

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