Question

The outer diameter of a gas cylinder is 20 cm. Find the cost of painting of its outer curved surface at ₹ 4 per cm square if the height of the cylinder is 70 cm square.​

Answer 1

Answer:

Given,Outer diameter = 20cm

Therefore,Radius,r=20cm/2=10cm

Height,h=70cm

Therefore,CSA=2×22/7×10×70

=4400cm square

Therefore,cost of painting its outer curved surface at ₹ 4 per cm square=4400cm square ×4

=17600cm square.

Step-by-step explanation:

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Answer 2

What we have to do ?

We are given the outer diameter of a gas cylinder is 20 cm and it's height is 70 cm² respectively. Cost of painting per cm² is ₹ 4. For finding total cost first we will find radius then curved surface area and therefore simply multiplying it with the per cm cost.Let's do it :-

Curved surface area of a Cylinder :-

$\bf{\underline{CSA = 2 \pi rh}}$

Where :-

• r = Radius of the cylinder

• h = Height of the cylinder

According to the Question :

Have to find the radius of the base of the cylinder first.

We Know that ,

$\Rightarrow \bf{Radius = \dfrac{Diameter}{2}}$

Given , Diameter = 20 cm.

Putting the value in the diameter , we get :

$\implies \bf{Radius = \dfrac{Diameter}{2}} \\ \\ \implies \bf{Radius = \dfrac{20}{2}} \\ \\ \implies \bf{Radius = 10 cm}$

Hence the Radius of the Cylinder is 10 cm.

Finding CSA of cylinder :-

$\dashrightarrow\:\:\sf Curved \: surface \: of \: cylinder = 2 \times \pi \times r \times h$

• Radius = 10 cm

• Height = 70 cm

The value of π is taken as 22/7 , if the value is not mentioned in the question.

Now , using the formula :-

Substituting the respective values, we get :

$\dashrightarrow\:\:\sf Curved \: surface \: of \: cylinder = 2 \times \dfrac{22}{7} \times 10 \times 70$

$\dashrightarrow\:\:\sf Curved \: surface \: of \: cylinder = \dfrac{44}{7} \times 10 \times 70$

$\dashrightarrow\:\:\sf Curved \: surface \: of \: cylinder = \dfrac{440}{7} \times 70$

$\sf \longrightarrow \: CSA \: = {\dfrac{440}{ \cancel{7}^{ \: \: 1} } \times \cancel{70}^{ \: \: 10} \:}$

$\dashrightarrow\:\:\sf Curved \: surface \: of \: cylinder = 440 \times 10$

$\dashrightarrow\:\:\bf Curved \: surface \: of \: cylinder = 4400 cm^{2}$

For Finding Total cost :-

Curved surface area × Per cm cost

• Curved surface area → 4400 cm²

• Per cm cost → 4 Rupees

Total cost = 4400 × 4

Total cost = 17600 Rupees

Hence,

$\dashrightarrow\:\: \underline{ \boxed{\sf Total \: cost \: for \: painting \: = 17600 \: Rupees }}$

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