a sphere of diameter 6cm is dropped in a right circular cylindrical vessel partly filled with water the - Maths - Surface Areas and Volumes

Question

a sphere of diameter 6cm is dropped in a right circular
cylindrical vessel partly filled with water the diameter of the
cylindrical vessel is 12cm if sphere is completely submerged in
water by how much will the level of water rise?

Ankush Jain · Accepted Answer

Here, the volume increased in the cylindrical vessel will be equal to the volume of sphere.

Given, the diameter of sphere = 6 cm

⇒ radius of sphere = R = 6/2 = 3 cm

Similarly, diameter of cylindrical vessel = 12 cm

⇒ radius of cylindrical vessel = r = 12/2 = 6 cm

Now, volume of sphere $= \frac{4}{3} π R^{3} = \frac{4}{3} π {(3)}^{3}$

and volume of cylindrical vessel $= π r^{2} h = π {(6)}^{2} h$

$\Rightarrow \frac{4}{3} π {(3)}^{3} = π (6)^{2} h \Rightarrow h = \frac{4 \times 3 \times 3 \times 3}{3 \times 6 \times 6} = 1 c m$

Hence, the water level will rise by 1 cm.

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a sphere of diameter 6cm is dropped in a right circular cylindrical vessel partly filled with water . the diameter of the cylindrical vessel is 12cm. if sphere is completely submerged in water by how much will the level of water rise?