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Question

# Calculate the weight density of a block of material $4.27$ in. $\times 3.87$ in. $\times 5.44$ in. that weighs $0.982 \mathrm{lb}$.

Solution

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$\textbf{Given:}$

$F_W= .982 \text{ lb}$

$a=4.27 \text{ in}$

$b=3.87 \text{ in}$

$c=5.44 \text{ in}$

To find the expression and calculate the weight density of the object which is by definition given as

$D_W=\dfrac{F_W}{V}$

we must first determine the volume. We do it by using a simple formula for the volume of a square:

$V=a\cdot b \cdot c$

We now calculate it by including the data given in the task:

\begin{align*} V&=4.27 \cdot 3.87 \cdot 5.44\\ &= 89.9 \text{ in}^3\\ &\boxed{V=0.052 \text{ ft}^3} \end{align*}

We proceed with the calculation of weight density:

\begin{align*} D_W&=\dfrac{F_W}{V}\\ &=\dfrac{0.982}{0.052 }\\ &\boxed{D_W=18.9 \text{ } \dfrac{\text{lb} }{ \text{ft}^3} } \end{align*}

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