Question

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 rocked is 26 cm, while the height of the conical art is 6cm. The base of the conical position 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 is to be painted yellow, find the area of the rocket painted with each of these color (Take π = 3.14)

Answer 1

Dear Student,

Answer:
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Orange colour = 51.05 sq-cm
Yellow color= 188.49 sq-cm

Solution:
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Curved surface area of cone = π r l

Here r (radius) = 2.5 cm

Since radius is half of Diameter.

l = slant height

from right angle triangle as mentioned in the diagram ,l is hypotenuse,it can be calculated by Pythagoras theorem.
$l = \sqrt{ {r}^{2} + {h}^{2} } \\ \\ l = \sqrt{ {(2.5)}^{2} + {(6)}^{2} } \\ \\ l = \sqrt{42.25 } \\ \\l = 6.5 \: \: cm$
A.T.Q conical part is to painted orange ,So orange colour is required to paint CURVED SURFACE AREA of cone

=
$= \pi \: \times 2.5 \times 6.5 \: {cm}^{2} \\ = 51.05 \: {cm}^{2}$
The part if the rocket to be painted yellow,is the CSA of cylindrical shape = 2πrh
here h (height) = 20 cm

Radius (r) = 1.5 cm
$= 2 \times \pi \times 20 \times 1.5 \: {cm}^{2} \\ = 188.49 \: {cm}^{2}$
Orange paint to be painted on 51.05 sq-cm area,
Yellow paint to be painted on 188.49 sq-cm area.

Hope it helps you.
Thanks for asking such a nice question.

Answer 2

Let r be the radius of the base of the

cone and it's slant height be ' l ' .

Let r1 be the radius of cylinder and h1

be it's height

We have ,

r = 2.5 cm , h = 6 cm

r1 = 1.5 cm , h1 = 20 cm

Now ,

l = √ r² + h²

=> l = √ ( 2.5 )² + 6²

l = √ 6.25 + 36

l = √ 42.25

l = 6.5 cm

Now ,

area to be painted orange CSA of

the cone + base area of the cone

- base area of the cylinder


= πrl + πr² - πr1²

= π{ 2.5×6.5)+(2.5)² - ( 1.5 )² } cm²

= π ( 20.25 ) cm²

= 3.14 × 20.25 cm²

= 63.585 cm²

Area to be painted yellow

= CSA of the cylinder + Area of base of

the cylinder

= 2πr1h1 + πr1²

= πr1( 2h1 + r1 )

= 3.14 × 1.5 ( 2 × 20 + 1.5 ) cm²

= 3.14 × 1.5 × 41.5 cm²

= 4.71 × 41.5 cm²

= 195.465 cm²

Therefore ,

area to be painted yellow = 195.465 cm²

I hope this helps you.

: )