A wooden block of dimensions of 6 cm ⨯ 6 cm ⨯ 15 cm floats with the long axis oriented horizontally and the of the square faces are oriented so that they point up vertically, straight up out of the water like a diamond shape. If the wooden block is submerged to a depth 7.96 cm (the bottom point to the water level), then: (a) What is the submerged volume of the block?(b) What is the mass of the block
(c) What is the density of the block?

Explanation:

(a)  Formula to calculate volume of the submerged wooden block is as follows.

It is given data of the wooden block is as follows.

          depth = 7.96 cm,       length (l) = 6 cm

         width (w) = 4 cm,      

So, we will calculate the volume of the submerged wooden block as follows.

                       =

                       = 286.56  

Hence,  the submerged volume of the block is 286.56  .

(b)   Expression for the buoyant force acting on the wooden block is as follows.

And, expression for the force of gravity of the wooden block is as follows.

As the wooden block is floating on the water hence, buoyant force is balanced by the weight of the block.

Hence, mass of the wooden block will be calculated as follows.

                      =

                      =

                      = 0.02857 kg

Therefore, mass of the given block is 0.02857 kg

(c)   Expression for the density of the block is as follows.

Now, expression for the total volume of the wooden block is as follows.

Hence, density of the given block is as follows.

                         =

                         =

                         =

Therefore, density of the given block is .

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