(Q2)A wooden toy rocket is in the shape of a cone mounted on a cylinder as shown in the adjacent figure. The height of the entire rocket is 26 cm, while the height of the conical part is 6 cm. The base of the conical position 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 is to be painted yellow, find the area of the rocket painted with each of these color(Take π = 3.14)

26 cm6 cm3cmBase of cylinderBase of cone5 cm

Let 'r' be the radius of the base of the cone and its slant height be. Further, let r1 be the radius of cylinder and h1 be its height. We have,

r = 2.5 cm , h = 6 cm

r1 = 1.5 cm, h1 = 20 cm

Now, l = √(r2 + h2)

⇒ l = √( 2 + 2)

⇒ l = √( + ) = √( ) =

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

= πrl + πr2 - πr12

= π ( rl + r2 - r12 )

= π{( × ) + ( )2 - ( )2} cm2

= π( ) cm2 = 3.14 × cm2 = cm2

Area to be painted yellow = Curved surface area of the cylinder + Area of the base of the cylinder

= 2πr1h1 + πr12

= πr1(2h1 + r1)

= 3.14 × (2 × + )cm2

= 3.14 × × cm2

= × cm2

= cm2

Therefore, area to be painted yellow = cm2