Question

a wooden toy rocket is in the shape of a a cone mounted on a cylinder.The height of the entire rocket is 26 cm,while the height of the conical is 6 CM, the base of the conical portion has a diameter of 5 cm, wile base diameter of the cylinder portion is 3 cm conical portion is to be painted orange and cylindrical pots and yellow, find the area of the rocket painted with each of this colours (use pie 3.14 )​

Answer 1

Answer -

Yellow colour = 188.49 cm²

Orange colour = 51.03 cm²

$\rule{200}2$

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 if 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 is 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 yellow and orange colour.

Solution:-

[ Refer the attachment for figure ]

Curved surface area of cone = πrl

→ 3.14 × 2.5 × l

→ 7.85 × l ...(1)

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) in (1)

→ 7.85 × 6.5

→ 51.03 cm²

Now,

Curved surface area of cylinder = 2πrh

→ 2 × 3.14 × 20 × 1.5

→ 188.49 cm²

Answer 2

$\LARGE\underline{\underline{\sf \red{T}\blue{o}\:\green{F}\orange{i}\pink{n}\red{d}:}}$

• area of rocket painted with orange (conical)
• area of rocket painted with yellow (cylinder)

$\LARGE\underline{\underline{\sf \red{G}\blue{i}\green{v}\orange{e}\red{n}:}}$

• Height of entire rocket = 26cm
• height of cone = 6cm
• Height of cylinder = 26-6 = 20cm
• Diameter of conical base = 5cm
• Radius of conical base = D/2 =2.5cm
• Diameter of cylinder portion = 3cm
• Radius of cylinder portion = 1.5cm

$\huge\boxed{\fcolorbox{fuchsia}{grey}{Solution:--}}$

$\textsf{see diagram in image first .}$

First we have to find slant Height of cone .

Slant Height = √(radius²+height²)

$l = \sqrt{( {6}^{2}) + ( {2.5}^{2}) } \\ \\ l = \sqrt{36 + 6.25 } \\ \\ l = \sqrt{42.25} \\ \\ l = 6.5 \: cm$

Now, area of rocket painted with orange (conical) = Curved surface area of cone = πrl (π = 3.14)

so, required area = 3.14 × 2.5 × 6.5 = $\large\red{\boxed{\sf </strong><strong>5</strong><strong>1</strong><strong>.</strong><strong>0</strong><strong>2</strong><strong>5</strong><strong>\</strong><strong>:</strong><strong>cm^</strong><strong>{</strong><strong>2</strong><strong>}</strong><strong>}}$

______________________________

Now,

area of rocket painted with yellow (cylinder) = curved surface area of cylinder = 2πrh

so, Required Area = 2 × 3.14 × 1.5 × 20 = $\large\red{\boxed{\sf 188.4\:cm^{2}}}$

______________________________

$\color {red}\large\bold\star\underline\mathcal{Extra\:Brainly\:Knowledge:-}$

1) TSA of cone = πr(r+l)

2) Volume of cone = 1/3 πr²h

3) TSA of cylinder = 2πr(h+r)

4) Volume of cylinder = πr²h