A rectangular wooden block measures 10.0cm x 4.00cm x 2.00cm. when the block is placed in water, it floats horizontally, with its bottom face 1.65cm below the surface. what is the density of the wood? show and explain your work.

The density of the wood is

ρ₂ = 1.21 g / cm³

Explanation:

The block measures

V₁ = 10.0 cm * 4.0 cm * 2.0 cm

V₁ = 80 cm³

Now the block measures under the water getting just the face below as 1.65 cm

V₂ = 10.0 cm * 4.0 cm * 1.65 cm

V₂ = 66 cm³

So to determine the density knowing the mass are the same as the weight

ρ₁ * V₁ = ρ₂ * V₂

Using the density of the water as a

ρ₁ = 1 g / cm ³

1 g / cm³ * 80 cm ³ = ρ₂ * 66 cm³

ρ₂ = 1.21 g / cm³