Question

A wood block, 10 in x 6.0 in x 2.0 in, "weighs" 3 lb 10 oz. What is the density of the wood?

Answer 1

Answer on Question#74678 – Chemistry – General chemistry

Question: A wood block, 10 in x 6.0 in x 2.0 in, "weighs" 3 lb 10 oz. What is the density of the wood?

Solution:

1. Find the volume of the wood block in $\mathrm{cm}^3$.

$$\begin{array}{l} 1 \text{ in} = 2.54 \text{ cm} \\ 10 \text{ in} = 10 \times 2.54 \text{ cm} = 25.4 \text{ cm} \\ 6.0 \text{ in} = 6.0 \times 2.54 \text{ cm} = 15.24 \text{ cm} \\ 2.0 \text{ in} = 2.0 \times 2.54 \text{ cm} = 5.08 \text{ cm} \\ \end{array}$$ $$V(\text{wood block}) = 25.4 \text{ cm} \times 15.24 \text{ cm} \times 5.08 \text{ cm} = 1966.45 \text{ cm}^3.$$

2. Find the mass of the wood block in g.

$$\begin{array}{l} 1 \text{ lb} = 16 \text{ oz} \\ 3 \text{ lb} = 3 \times 16 \text{ oz} = 48 \text{ oz} \\ 3 \text{ lb } 10 \text{ oz} = 48 \text{ oz} + 10 \text{ oz} = 58 \text{ oz} \\ 1 \text{ oz} = 28.35 \text{ g} \\ \end{array}$$ $$m(\text{wood block}) = 58 \text{ oz} = 58 \times 28.35 \text{ g} = 1644.3 \text{ g}$$

3. Find the density of the wood block.

$$d = \frac{m(\text{wood block})}{V(\text{wood block})} = \frac{1644.3 \text{ g}}{1966.45 \text{ cm}^3} = 0.84 \frac{\text{g}}{\text{cm}^3}$$

Answer: $0.84 \text{ g/cm}^3$

Answer provided by AssignmentExpert.com