A rectangular wooden block measures $10.0 \mathrm {~cm} \times 4.00 \mathrm {~cm} \times 2.00 \mathrm {~cm}$
When the block is placed in water, it floats horizontally, with its bottom face 1.65 cm below the surface. What is the density of the wood? The density of water is $1.00 \mathrm {~g} / \mathrm { cm } ^ { 3 }$
A) $1.65 \mathrm {~g} / \mathrm { cm } ^ { 3 }$
B) $0.350 \mathrm {~g} / \mathrm { cm } ^ { 3 }$
C) $0.825 \mathrm {~g} / \mathrm { cm } ^ { 3 }$
D) $1.21 \mathrm {~g} / \mathrm { cm } ^ { 3 }$
E) $0.606 \mathrm { a } / \mathrm { cm } ^ { 3 }$

Question

A rectangular wooden block measures $10.0 \mathrm {~cm} \times 4.00 \mathrm {~cm} \times 2.00 \mathrm {~cm}$
When the block is placed in water, it floats horizontally, with its bottom face  1.65 cm below the surface. What is the density of the wood? The density of water is $1.00 \mathrm {~g} / \mathrm { cm } ^ { 3 }$
A) $1.65 \mathrm {~g} / \mathrm { cm } ^ { 3 }$
B) $0.350 \mathrm {~g} / \mathrm { cm } ^ { 3 }$
C) $0.825 \mathrm {~g} / \mathrm { cm } ^ { 3 }$
D) $1.21 \mathrm {~g} / \mathrm { cm } ^ { 3 }$
E) $0.606 \mathrm { a } / \mathrm { cm } ^ { 3 }$

Quizplus · Accepted Answer

The density of the wood can be found by using the principle of buoyancy, which states that the weight of the displaced water is equal to the weight of the object. The volume of water displaced is equal to the submerged volume of the block, which is $10.0 \mathrm{cm} \times 4.00 \mathrm{cm} \times 1.65 \mathrm{cm} = 66.0 \mathrm{cm}^3$. The mass of the displaced water is its volume times the density of water ($66.0 \mathrm{cm}^3 \times 1.00 \mathrm{g/cm}^3 = 66.0 \mathrm{g}$). The total volume of the wood is $10.0 \mathrm{cm} \times 4.00 \mathrm{cm} \times 2.00 \mathrm{cm} = 80.0 \mathrm{cm}^3$. The density of the wood is the mass of the displaced water (which equals the mass of the wood) divided by the total volume of the wood, $66.0 \mathrm{g} / 80.0 \mathrm{cm}^3 = 0.825 \mathrm{g/cm}^3$.

A Rectangular Wooden Block Measures 10.0 cm×4.00 cm×2.00 cm10.0 \mathrm {~cm} \times 4.00 \mathrm {~cm} \times 2.00 \mathrm {~cm}10.0 cm×4.00 cm×2.00 cm

A Rectangular Wooden Block Measures $10.0 \mathrm {~cm} \times 4.00 \mathrm {~cm} \times 2.00 \mathrm {~cm}$