a steel hex nut has two regular hexagonal faces and a hole with a diameter of 0.4 cm through the middle. its…

Explanation:

Step1: Calculate prism volume

Let's assume the apothem of the hexagon is $a$ and side - length is $s$. The perimeter of a regular hexagon $P = 6s$. The area of a regular hexagon $A=\frac{1}{2}aP$. Suppose the height of the prism $h = 0.8+0.6=1.4$ cm. If we assume the side - length of the hexagon $s = 0.5$ cm and apothem $a=\frac{\sqrt{3}}{2}s$. Then $P = 6s = 3$ cm and $A=\frac{1}{2}aP=\frac{1}{2}\times\frac{\sqrt{3}}{2}\times0.5\times3=\frac{3\sqrt{3}}{8}$ cm². The volume of the prism $V_{prism}=A\times h=\frac{3\sqrt{3}}{8}\times1.4=\frac{2.1\sqrt{3}}{4}\approx0.91$ cm³.

Step2: Calculate cylinder volume

The formula for the volume of a cylinder is $V_{cylinder}=\pi r^{2}h$. Given diameter $d = 0.4$ cm, so radius $r=\frac{d}{2}=0.2$ cm and height $h = 1.4$ cm. Then $V_{cylinder}=\pi\times(0.2)^{2}\times1.4=\pi\times0.04\times1.4 = 0.056\pi\approx0.18$ cm³.

Step3: Calculate composite - figure volume

$V = V_{prism}-V_{cylinder}\approx0.91 - 0.18=0.73$ cm³.

Step4: Calculate density

The mass $m = 3.08$ grams. The density formula is $d=\frac{m}{V}$. So $d=\frac{3.08}{0.73}\approx4.22$ g/cm³.

Answer:

1. $0.91$
2. $0.18$
3. $0.73$
4. $4.22$