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There is water to a height of 14 cm in a cylindrical glass jar of radius 8 cm. Inside the water there is a sphere of diameter 12 cm completely immersed. By what height will the water go down when the sphere is removed ?

Mensuration

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Answer

Given, radius of glass jar = R = 8 cm

Diameter of sphere = 12 cm

Radius of sphere = r = 122\dfrac{12}{2} = 6 cm.

When the sphere is removed from the jar, volume of water decreases.

Let h be the height by which water level decrease.

Volume of water decreased = Volume of sphere.

⇒πR2h=43πr3⇒82h=43×63h=4×633×82h=4×2163×64h=864192h=4.5 cm.\Rightarrow πR^2h = \dfrac{4}{3}πr^3 \\[1em] \Rightarrow 8^2h = \dfrac{4}{3} \times 6^3 \\[1em] h = \dfrac{4 \times 6^3}{3 \times 8^2} \\[1em] h = \dfrac{4 \times 216}{3 \times 64} \\[1em] h = \dfrac{864}{192} \\[1em] h = 4.5 \text{ cm}.

Hence, the height by which water level rises is 4.5 cm.

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