Question

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 1

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 = 5/2 = 2.5 cm

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