Question

A wooden rocket is in the form of a cone mounted ona cylinder.The height of the entire rocket is 26cm.,while the height of the conical part is 6xm the base of the conical portion has a diameter of 5cm. while the base diameter of the cylindrical portion is 3 cm. If the conical portion is to be painted orange ans the cylindrical portion yellow , find the area of the rocket painted with each of these colour(use
$\pi = 3 .14)$
3.14)

Answer 1

Hey there!

Let ‘r’ be the radius of the base of the cone and its slant height be ‘l’. 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
  = √(2.5)² + (6)²
  = √42.25

Now, area to be painted orange = Curved surface area of the cone

                                                   = πrl

                                                   = 3.14 {2.5 × 6.5} 

                                                   = 51.025 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 × 1.5 (2×20+1.5)

                                         = 3.14 × 1.5 × 41.5

                                         =  4.71 × 41.5

                                         = 195.465 cm²

HOPE IT HELPED ^_^

Answer 2

$\huge\sf{\underline{\underline{Solution:}}}$

Answer:-

Yellow colour = 188.49 cm²

Orange colour = 51.03 cm²

$\sf\underline{\underline{STEP-BY-STEP-EXPLANATION}}$

Given:-

• A wooden toy rocket is in the shape of a a cone mounted on a cylinder.

• For cone ,height is 6 cm and radius is 2.5 cm. (diameter = 5 cm)

• For cylindrical base part :- height is 20 cm and radius is 1.5 cm (diameter = 3 cm)

• Total height of the toy = 26 cm.

• Conical part of toy is painted with yellow colour and cylindrical part is painted with orange colour.

Find:-

• Portion to be painted with colours.

______________________________

Curved surface area of cone = πrl

 3.14 × 2.5 × l

7.85 × l 

Now

l = √(r² + h²)

l = √[(2.5)² + (6)²]

l = √6.25 + 36

l = √42.25

l = 6.5 cm

Put value of l (slant height)

7.85 × 6.5

51.03 cm²

Now,

Curved surface area of cylinder = 2πrh

2 × 3.14 × 20 × 1.5

$\huge\boxed{188.49 cm^2}$