Question

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 cm. Find the diameter of
the cylindrical vessel.

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Answer 1

Answer:

Increase in the height of the cylinder due to the sphere, h = 3\dfrac{5}{9}=\dfrac{32}{9}h=395=932 cm

Diameter of sphere = 12=12 cm

Radius of the sphere, R = 6R=6 cm

Rise in the volume of water in cylinder == Volume of sphere

\pi r^2h = \dfrac{4}{3}\pi R^3πr2h=34πR3

r = \sqrt{\dfrac{4\times 6^3\times 9}{3\times 32}}r=3×324×63×9

\therefore r = 9∴r=9 cm

Therefore, the diameter of the cylindrical vessel = 18=18 cm.

Answer 2

Answer:

Step-by-step explanation:

ncrease in the height of the cylinder due to the sphere= h=395=932 cm

Diameter of sphere = 12=12 cm

Radius of the sphere, R = 6R=6 cm

Rise in the volume of water in cylinder == Volume of sphere

R^3πr2h=34πR3

R=3×324×63×9

therefore r = 9∴r=9 cm

Therefore, the diameter of the cylindrical vessel = 18=18 cm.