One sphere of diameter 18 cm is dropped in a cylindrical vessel of diameter 36 cm, partially filled with water. If the sphere is completely immersed in water, find the rise in the level of water.

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One sphere of diameter 18 cm is dropped in a cylindrical vessel of diameter 36 cm, partially filled with water. If the sphere is completely immersed in water, find the rise in the level of water.

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answer is A.

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Detailed Solution

Given,
The sphere's diameter

r_{s} = \frac{18}{2} cm = 9 cm

Cylindrical diameter

r_{c} = \frac{36}{2} cm = 18 cm

Let the rise in water level in the cylindrical vessel = h cm.
Now, Sphere's volume

V_{s} = \frac{4}{3} π r^{3}

Displaced liquid volume in cylindrical vessel

V_{w} = π R^{2} h

Here,
Displaced liquid volume in the cylindrical vessel = Sphere's volume
Here,

π R^{2} h = \frac{4}{3} π r^{3}

(18)^{2} \times h = \frac{4}{3} \times (9)^{3}

h = \frac{4 \times (9)^{3}}{3 \times (18)^{2}}

h = 3 cm

So, rise in water level in cylindrical vessel = 3 cm.
Correct option is 1.

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