Question

A cylindrical container with diameter of base 56 cm contains sufficient water to submerge a rectangular solid of iron with dimensions 32 cm×22 cm× 14 cm. Find the rise in the level of the water when the solid is completely submerged.

Answer 1

The rise in the level of the water when the solid is completely submerged is 4 cm

Step-by-step explanation:

• Given data

        Diameter of cylinder (D) = 56 cm

        So radius of cylinder (R) = 28 cm

        Length of rectangular solid (L) = 32 cm

        Breadth of rectangular solid (B) = 22 cm

        Height of rectangular solid (H) = 14 cm

        Let rise in water level of cylinder = h   cm

• When rectangular solid is submerged in water , it will displaced volume of water equal to itself volume.

• We can say that

        Volume of water displaced = Volume of rectangular solid     ...1)

• Where

      Volume of rise of water in cylinder = Volume of water displaced

       From equation 1) above equation can be written as

       Volume of rise of water in cylinder =Volume of rectangular solid  

       $\mathbf{\pi \times R^{2}\times h=L\times B\times H}$    ...2)

       $\mathbf{Where \ \left ( \pi =\frac{22}{7} \right )}$

       On putting respective value in equation 2)

       $\mathbf{\frac{22}{7} \times 28^{2}\times h=32\times 22\times 14}$

       So

       $\mathbf{h=\frac{32\times 22\times 14\times 7}{22\times 28\times 28} =4 \ cm}$= This is value of rise of water level.