TITLE: How is volume equal to length of block here?
QUESTION [2 upvotes]: Here we have a block submerged in water.Density of water = 1000 and of air = 0.density of block = 800.
Then , we have written the equation for downward force = g * V * 800 - g{( Ax(amount of area of that block in air I.e x) * x(length of block)*0 + Ay (1000)(y)}.
I didn’t understand why is V = x+y here ?
I thought for a while over it and saw maybe that it is done in this way that :
V of block / area of block with y length.Now , even if that is done.How can we compare area of only y portion of block in water with whole volume of block?

REPLY [3 votes]: It's a mistake. The equation
$$(x+y)800 = Ay1000$$
should be
$$A(x+y)800 = Ay1000$$
Notice that the $A$ on the right side of the equation disappears in the next line:
$$8x + 8y =10y$$
{"set_name": "stack_exchange", "score": 2, "question_id": 603092}