Mathematics

A cylindrical container with diameter of base 42 cm contains sufficient water to submerge a rectangular solid of iron with dimensions 22 cm × 14 cm × 10.5 cm. Find the rise in level of the water when the solid is submerged.

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Given,

Diameter of base of cylindrical container = 42 cm

Radius of base of cylindrical container (r) = $\dfrac{42}{2}$ = 21 cm.

Let rise in level of water be h cm.

∴ Volume of solid submerged = Volume of increased water

⇒ 22 cm × 14 cm × 10.5 cm = πr²h

⇒ 3234 = $\dfrac{22}{7} \times 21^2 \times h$

⇒ h = $\dfrac{3234 \times 7}{22 \times 21^2}$

⇒ h = $\dfrac{22638}{9702} = 2\dfrac{1}{3}$ cm.

Hence, water rises by $2\dfrac{1}{3}$ cm in container.

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