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Mathematics

A metal cube of side 11 cm is completely submerged in water contained in a cylindrical vessel with diameter 28 cm. Find the rise in the level of water.

Mensuration

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Answer

Given,

⇒ Diameter = 28 cm

⇒ Radius (r) = 14 cm

⇒ Side of cube (a) = 11 cm.

Let the rise in level of water be h cm.

So, the volume of water risen = volume of cube

∴ πr2h = a3

⇒227×(14)2×h=(11)3⇒h=11×11×11×722×14×14⇒h=93174312⇒h=2.16 cm.\Rightarrow \dfrac{22}{7} \times (14)^2 \times h = (11)^3 \\[1em] \Rightarrow h = \dfrac{11 \times 11 \times 11 \times 7}{22 \times 14 \times 14} \\[1em] \Rightarrow h = \dfrac{9317}{4312} \\[1em] \Rightarrow h = 2.16 \text{ cm}.

Hence, rise in level of water = 2.16 cm.

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