A sphere of diameter 12 cm, is dropped in a right circular cylindrical vessel, partly filled with water. If the sphere is completely submerged in water, the water level in the cylindrical vessel rises by 3 `5/9` cm. Find the diameter of the cylindrical vessel.

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#### Solution

Radius of sphere = r = 6 cm

Volume of sphere = `4/3pir^3=4/3pixx(6)^3 = 288pi ""cm^3`

Let R be the radius of cylindrical vessel.

Reise in the water level of cylindrical vessel = `h=3 5/9 "cm" = 32/9 "cm"`

Increase in volume of cylindrical vessel = `piR^2h=piR^2xx32/9=32/9piR^2`

Now, volume of water displaced by the sphere is equal to volume of sphere.

`:.32/9piR^2=288pi`

`:. R^2=(288xx9)/32=81`

∴ R = 9 cm

∴ Diameter of the cylindrical vessel 2xR = 2x9 =18 cm

Concept: Concept of Surface Area, Volume, and Capacity

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