Q. 163.7( 11 Votes )

A wooden toy rocket is in the shape of a cone mounted on a cylinder, as shown in the given figure. The height of the entire rocket is 26 cm, 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 colours. [Take π=3.14]


Answer :


The area to be painted orange


= CSA of cone + Base area of Cone – Base area of the cylinder


Curved Surface Area of Cone


Given that diameter of conical portion = 5cm


The radius of conical portion


Height of the conical part = h = 6cm


We need to find the ‘l’ first


We know that


l2 = h2 + r2


l2 = 62 + (2.5)2


l2 = 36 + (6.25)


l2 = 42.25


l = √42.25


l = 6.5cm


So, CSA of conical portion = πrl


=3.14×2.5×6.5


= 51.025 cm2


Base area of the cone = πr2


=3.14×2.5×2.5


=19.625 cm2


Diameter of the cylinder = 3cm


So, Radius of the cylinder = 1.5cm


Base area of the cylinder = π(r’)2


=3.14×1.5×1.5


=7.065 cm2


So, the area to be painted orange = 51.025 + 19.625 – 7.065


= 63.585 cm2


Now, the area to be painted yellow


= CSA of the cylinder + Area of one bottom base of the cylinder


= 2πr’h’ + π(r’)2


= 2 × 3.14 × 1.5 × 20 + 7.065


= 188.4 + 7.065


= 195.465 cm2


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