Question

The cost of painting the total outside surface of a closed cylindrical tank at 60 paise per meter squae is Rs237.60. The height of the tank is six times the radius of the base of the tank, find its volume correct to two decimal places.

Answer 1

`volume=509.25 dm^(3)`

Explanation:

Curved surface area=
`\frac {237.6}{0.6}=396 dm^(2)=2\pi R(R+H)` where R is radius and H is height

Since H=6R then curved surface area=
`2\pi R(R+6R)=14\pi R^(2)`

Therefore,

`396 dm^(2)=14\pi R^(2)` and making R the subject

`R=\sqrt {\frac {396}{14\pi}}=\sqrt {(9.003622)}= 3.000604 m`

Therefore, H=6R=6*3.000604=18.00362 m

`Volume=\pi R^(2)H=\pi*3.000604^(2)*18.00362=509.2453 dm^(3)`

Therefore,
`volume=509.25 dm^(3)`