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प्रश्न
The cost of painting the total outside surface of a closed cylindrical oil tank at 50 paise per square decimetre is Rs 198. The height of the tank is 6 times the radius of the base of the tank. Find the volume corrected to 2 decimal places.
उत्तर
Data given is as follows:
h = 6r
Total cost of painting=Rs.198
Painting rate= Rs.0.50 per square decimeter
We have to find the volume of the cylinder.
We know that,
Total Surface Area of the cylinder = `2pirh + 2pir^2`
Also, it is given that,
Total cost of painting = 198
That is,
(Total Surface Area of the cylinder ) × Painting rate = 198
`( 2pirh + 2pir^2 ) xx ` Painting rate = 198
`(2 pi rh + 2 pir^2) xx 0.50 = 198 `
`(2pirh +2pir^2) = 396`
In the above equation, let us replace h with 6r.
` 12 pir^2 + 2pir^2`=396
`14 pir^2`=396
`14 xx 22/7 xx r^2`=396
r =3 decimeters
h = 6r = 6 × 3 =18 decimeters
Volume of the cylinder = `pir^2h`
`=22/7 xx 3 xx 3xx 18`
Volume of the cylinder = 509.14dm3
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