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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 :
- radius of the vessel.
- height of the vessel.
- wetted surface area of the vessel when it is half-filled with water.
Solution
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
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