Question

3080 cm³ of water is required to fill a cylindrical vessel completely and 2310 cm³ of water is required to fill it upto 5 cm below the top. Find : 

1. radius of the vessel.
2. height of the vessel.
3. wetted surface area of the vessel when it is half-filled with water.

Answer 1

Let r be the radius of the cylindrival vessel and h be its height

Now, volume of cylindrical vessel = volume of water filled in it

`=>` πr²h = 3080

`=> 22/7 xx r^2 xx h = 3080`

`=>` r² × h = 980  ...(i)

Volume of cylindrical vessel of height 5 cm = (3080 – 2310) cm³

`=>` πr² × 5 = 770

`=> 22/7 xx r^2 xx 5 = 770`

`=>` r² = 49

`=>` r = 7 cm

Substituting r² = 49 in (i), we get

49 × h = 980

`=>` h = 20 cm

Wetted surface area of the vessel when it is half-filled with water

= 2πrh + πr²

= πr(2h + r)

= `22/7 xx 7(2 xx 10 + 7)`   ...`["Half-filled" => "Height" = 20/2 = 10  cm]`

= 22 × 27

= 594 cm²