Answer

Verified

410.7k+ views

**Hint**: We can identify the value of various dimensions of both the cone and cylindrical figures constituting the toy rocket. Then applying formulas for the areas of respective figures, we can find the required areas to be painted by orange and yellow colors respectively.

Formulas to be used:

$l = \sqrt {{r^2} + {h^2}} $ where, l, r and h are the slant height, radius and height of the cone respectively.

Curved surface area of cone = $ \pi rl$

Curved surface area of cylinder = $ 2\pi rh$

Area of circle = $ \pi {r^2}$

**:**

__Complete step-by-step answer__We have been given:

Height of entire rocket = 26 cm

Height of conical part = 6 cm

Diameter of conical part = 5 cm

ğŸ¡ª Radius of conical part = $ \dfrac{5}{2} = 2.5cm$

(As diameter is equal to twice the value of radius)

Diameter of cylindrical part = 3 cm

Radius of cylindrical part = $ \dfrac{3}{2} = 1.5cm$

(As diameter is equal to twice the value of radius)

Slant height (l) of the cone can be calculated as:

$l = \sqrt {{r^2} + {h^2}} $ , here,

Radius (r) = 2.5 cm

Height (h) = 6 cm

$

\Rightarrow l = \sqrt {{{\left( {2.5} \right)}^2} + {6^2}} \\

\Rightarrow l = \sqrt {6.25 + 36} \\

\Rightarrow l = \sqrt {42.25} \\

\therefore l = 6.5 cm \;

$

Now, we have to paint conical portion as orange and the cylindrical portion as yellow:

Area to be painted as orange:

Curved surface area of cone + Base area of cone â€“ Base area of cylinder _____ (1)

Area to be painted as yellow:

Curved surface area of cylinder + One base area of cylinder _______ (2)

Finding the respective values:

i) Curved surface area of cone (CSA) = $ \pi rl$

Radius (r)= 2.5 cm

Slant height (l) = 6.5 cm

$

\Rightarrow CSA = 3.14 \times 2.5 \times 6.5\left( {\because \pi = 3.14} \right) \\

\therefore CSA = 51.025\;c{m^2} \\

$

ii) Base area of cone = Area of circle (as base is circular in shape)

Base area of cone (B.C)= $ \pi {r^2}$

Radius (r)= 2.5 cm

$

\Rightarrow BC = \pi {\left( {2.5} \right)^2} \\

\Rightarrow BC = 3.14 \times 6.25\left( {\because \pi = 3.14} \right) \\

\therefore BC = 19.625\;c{m^2} \\

$

iii) Curved surface area of cylinder (CSA) = $ 2\pi rh$

Radius (r) = 1.5 cm

Height (h) = height of entire rocket â€“ height of circular portion

$

\Rightarrow h = 26 - 20 \\

\therefore h = 20cm \\

$

$

\Rightarrow CSA = 2 \times 3.14 \times 1.5 \times 20 \\

\therefore CSA = 188.4 c{m^2} \\

$

ii) Base area of cylinder = Area of circle (as base is circular in shape)

Base area of cone (B.C)= $ \pi {r^2}$

Radius (r)= 1.5 cm

$

\Rightarrow BC = \pi {\left( {1.5} \right)^2} \\

\Rightarrow BC = 3.14 \times 2.25\left( {\because \pi = 3.14} \right) \\

\therefore BC = 7.065\; c{m^2} \;

$

Substituting the values in (1), we get:

Area to be painted as orange :

$

\Rightarrow \left( {51.025 + 19.625 - 7.0625} \right)c{m^2} \\

\Rightarrow \left( {70.65 - 7.0625} \right)c{m^2} \\

\therefore 63.58\; c{m^2} \;

$

Substituting the values in (2), we get:

Area to be painted as yellow :

$

\Rightarrow \left( {188.4 + 7.065} \right)c{m^2} \\

\therefore 195.465\; c{m^2} \;

$

Therefore, the area of the rocket painted with each orange and yellow colours are $ 63.58\;c{m^2}$ and $ 195.465\;c{m^2}$ respectively.

**Note**: As all the quantities were given in cm, we obtained the respective areas in $ c{m^2}$. In such questions we carefully observe which areas are required to be added and subtracted respectively to get the required area. In the curved surface areas of the bodies, we do not include their bases, it's like cutting the figure parallel to the base.

Recently Updated Pages

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Advantages and disadvantages of science

10 examples of friction in our daily life

Trending doubts

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Change the following sentences into negative and interrogative class 10 english CBSE

Difference Between Plant Cell and Animal Cell

Write a letter to the principal requesting him to grant class 10 english CBSE