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Question

Calculate the weight density of a block of material 4.274.27 in. ×3.87\times 3.87 in. ×5.44\times 5.44 in. that weighs 0.982lb0.982 \mathrm{lb}.

Solution

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Answered 2 years ago
Answered 2 years ago
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Given:\textbf{Given:}

FW=.982 lbF_W= .982 \text{ lb}

a=4.27 ina=4.27 \text{ in}

b=3.87 inb=3.87 \text{ in}

c=5.44 inc=5.44 \text{ in}

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

DW=FWVD_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=abcV=a\cdot b \cdot c

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

V=4.273.875.44=89.9 in3V=0.052 ft3\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:

DW=FWV=0.9820.052DW=18.9 lbft3\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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