Question

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.

Answer 1

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