Question

an irregular chunk of iron has a density of 7.87 g/cm³. a 14.5 gram chunk is added to a graduated cylinder. if the final volume of the graduated cylinder is 0.0394 l, what would be the starting volume?
22.5 ml
0.114 l
37.6 ml
1.84 ml

Explanation:

Step1: Calculate volume of iron chunk

Use density formula $
ho=\frac{m}{V}$, so $V = \frac{m}{
ho}$. Given $m = 14.5$ g and $
ho=7.87$ g/cm³, then $V=\frac{14.5}{7.87}\text{ cm}^3\approx1.84\text{ cm}^3$. Since $1\text{ cm}^3 = 1\text{ mL}$, the volume of the iron chunk is $1.84$ mL.

Step2: Convert final volume to mL

The final volume of the graduated - cylinder is $V_{final}=0.0394$ L. Since $1$ L = $1000$ mL, then $V_{final}=0.0394\times1000 = 39.4$ mL.

Step3: Calculate starting volume

Use the relationship $V_{final}=V_{starting}+V_{iron}$. Rearranging for $V_{starting}$ gives $V_{starting}=V_{final}-V_{iron}$. Substitute $V_{final} = 39.4$ mL and $V_{iron}=1.84$ mL, so $V_{starting}=39.4 - 1.84=37.6$ mL.

Answer:

37.6 mL