Math, asked by aksgeeta86, 8 months ago

a cylindrical pillar is 50 cm in diameter and 3.5 CM in height. find the cost of painting the curved surface area of the pillar at rate of rupees 12.50 per metre square.​

Answers

Answered by Anonymous
3

Given :

Diameter of the cylinder = 50 cm

Height of the cylinder = 3.5 cm

Cost of painting = Rs. 12.50 per m²

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

To Find :

The cost of painting the curved surface area of the cylindrical pillar !!

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Solution :

⠀⠀⠀Curved Surface area of the cylinder :

In the given information , the measures of the cylindrical pillar is in cm but the cost of painting in in m.

So first we have to convert all the units in m .

To covert a unit from cm to m , we should divide it by 100.

So let's covert height and diameter of the cylinder in m !!

Given the diameter is 50 cm , now multiplying it by 1/100 , we get :

⠀⠀⠀⠀⠀⠀⠀→ (50 × 1/100) m

⠀⠀⠀⠀⠀⠀⠀→ 1/2 m

⠀⠀⠀⠀⠀⠀⠀→ 0.5 m

Given the height is 3.5 cm, now multiplying it by 1/100 , we get :

⠀⠀⠀⠀⠀⠀⠀→ (3.5 × 1/100) m

⠀⠀⠀⠀⠀⠀⠀→ (35/10 × 1/100) m

⠀⠀⠀⠀⠀⠀⠀→ 35/1000 m

⠀⠀⠀⠀⠀⠀⠀→0.035 m

Hence, the diameter of the cylinder is 0.5 m and the Height of the cylinder is 0.035 m.

Now , let us find the radius of the cylinder !!

We know that ,

\bf{R = \dfrac{D}{2}}

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀Where :

⠀⠀⠀⠀⠀⠀⠀⠀⠀R = Radius

⠀⠀⠀⠀⠀⠀⠀⠀⠀D = Diameter

Now , Substituting the value of diameter in the formula , we get :

:\implies \bf{R = \dfrac{0.5}{2}} \\ \\

:\implies \bf{R = 0.25 m} \\ \\

\therefore \bf{Radius = 0.25 m} \\ \\

Hence, the radius of cylinder is 0.25 m.

Now , using the formula for curved surface area of a cylinder and substituting the values in it , we get :

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

:\implies \bf{CSA = 2 \times \dfrac{22}{7} \times 0.25 \times 0.035} \\ \\ \\

:\implies \bf{CSA = 2 \times \dfrac{22}{7} \times \dfrac{25}{100} \times \dfrac{35}{1000}} \\ \\ \\

:\implies \bf{CSA = 2 \times 22 \times \dfrac{25}{100} \times \dfrac{5}{1000}} \\ \\ \\

:\implies \bf{CSA = 22 \times \dfrac{25}{50} \times \dfrac{5}{1000}} \\ \\ \\

:\implies \bf{CSA = 22 \times \dfrac{1}{2} \times \dfrac{5}{1000}} \\ \\ \\

:\implies \bf{CSA = 11 \times \dfrac{5}{1000}} \\ \\ \\

:\implies \bf{CSA = 11 \times \dfrac{1}{200}} \\ \\ \\

:\implies \bf{CSA = 0.385 m^{2}} \\ \\ \\

\therefore \bf{Curved\:Surface\:Area = 0.385 m^{2}} \\ \\ \\

Hence, the curved surface area of the cylinder is 0.385 m².

⠀⠀⠀⠀⠀⠀⠀Cost of Painting :

Now , to find the cost of painting the curved surface area of the cylinder .

We have to find the product of the CSA and the cost on 1 per m² area (i.e, Rs. 12

50).

==> Rs. (CSA × 12.50)

==> Rs. (0.385 × 12.50)

==> Rs. 4.81

Hence, the cost of painting the curved surface area of the cylindrical pillar is Rs. 4.62.

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