Suppose that you place a square block of wood with dimensions 12.0 cm x 12.0 cm x 6.0 cm

into some water as shown below. The wood has a density of 600 kg/m3. What is the distance from the bottom horizontal face of the block to the surface of the
water? (In other words, how much of the block’s height will be underwater?)

figure the mass of the wood:

.12*.12*.06*600kg== 0.000864(600)= = 0.5184 kg

so now, the volume of water displaced must be 518cm
12*12*h=518 solve for h in cm

Vb = L*W*h = 12 * 12 * 6 = 864 cm^3. = Vol. of the block.

Db/Dw * h = 600/1000 * 6cm = 3.6 cm submerged.

NOTE: My vol. calculation was not required.

To find the distance from the bottom horizontal face of the block to the surface of the water, we need to calculate how much of the block's height will be underwater.

Step 1: Calculate the volume of the block
The volume of the block can be calculated using the formula:
Volume = length x width x height
Volume = 12.0 cm x 12.0 cm x 6.0 cm

Step 2: Convert the volume to cubic meters
To convert the volume from cubic centimeters (cm³) to cubic meters (m³), we need to divide the volume by 1,000,000 (since 1 m³ = 1,000,000 cm³).

Step 3: Calculate the mass of the block
The mass of the block can be calculated using the density formula:
Mass = density x volume

Step 4: Calculate the weight of the block
The weight of the block is the force acting on it due to gravity and can be calculated using the formula:
Weight = mass x acceleration due to gravity
The acceleration due to gravity is approximately 9.8 m/s².

Step 5: Calculate the buoyant force
The buoyant force acting on the block is equal to the weight of the water displaced by the block.

Step 6: Calculate the volume of water displaced
The volume of water displaced is equal to the volume of the block that is submerged in the water.

Step 7: Calculate the height of the submerged portion
The height of the submerged portion can be calculated by dividing the volume of water displaced by the cross-sectional area of the block.

Let's calculate the distance from the bottom horizontal face of the block to the surface of the water using these steps.