Let the radius, slant height and height of the cone be r,l,h and let the radius and height of the cylinder be r′,h′ respectively.
Then r=2.5cm,h=6cm,r′=1.5cm,h′=26−6=20cm
⇒l=√r2+h2=√(2.5)2+62=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 the cone(a ring) is to be painted.
So the area to be painted orange = Curved surface area of the cone + base area of the cone − base area of the cylinder.
=πrl+πr2−π(r′)2
=π[(2.5×6.5)+(2.5)2−(1.5)2]cm2
=π[20.25]cm2
=3.14×20.25cm2
∴ Area of the painted orange =63.585cm2
Now, the area to be painted yellow = Curved surface area of the cylinder + area of one base of the cylinder
=2πr′h′+π(r′)2
=πr′[2h′+r′]
=(3.14×1.5)(2×20+1.5)cm2
=4.71×41.5cm2
∴ Area to be painted yellow =195.465cm2