Question

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

Answer 1

Given :-

The outer diameter of a gas cylinder = 20 cm

The cost of painting of its outer curved surface = Rs. 4 per cm²

The height of the cylinder = 70 cm

To Find :-

The cost of painting of its outer curved surface.

Analysis :-

Firstly, find the radius by dividing the diameter by two.

Next find the curved surface area of the cylinder by substituting the given values in it's respective formula.

Once we find the CSA, we can find the cost of painting by multiplying it to the cost per centimeter square.

Solution :-

We know that,

• d = Diameter
• r = Radius
• h = Height
• CSA = Curved surface area

Finding the radius,

$\underline{\boxed{\sf Radius=\dfrac{Diameter}{2} }}$

Given that,

Diameter (d) = 20 cm

Substituting their values,

Radius = 20/2

Radius = 10 cm

By the formula,

$\underline{\boxed{\sf CSA \ of \ a \ cylinder=2 \pi rh}}$

Given that,

Radius (r) = 10 cm

Height (h) = 70 cm

Substituting their values,

= 2 × (22/7) × 10 × 70

By transposing 7,

= 2 × 22  × 10 × 70/7

= 2 × 22 × 10 × 10

= 4400 cm²

Therefore, the CSA of the cylinder is 4400 cm².

According to the question,

Cost for painting 1 cm square = Rs. 4

∴ Cost for painting 4400cm square = 4400 × 4

Cost = Rs. 17600

Therefore, the cost of painting is Rs. 17600.