Subtracting the volume of the cylinder from the volume of the prism, the volume of metal in the hex nut to the nearest tenth exists
<h3>How to estimate the
volume of metal in the
hex nut?</h3>
Diameter of the cylinder be d = 1.6 cm
Apothem of the hexagon be a = 2 cm
Thickness of the steel hex nut be t = 2 cm
Volume of the prism be 
Volume of the cylinder be 
Volume of metal in the hex nut,

To estimate the volume of a prism,

Ab = n L a / 2
Number of the sides, n = 6
The side of the hexagon be L
Height of the prism, h = t = 2 cm
Central angle in the hexagon, A = 360°/n
A = 360°/6 = 60°

simplifying the value of L, we get



Solving for L/2:

Solving the value of L, we get



Ab = n L a / 2
Substitute the values in the above equation, we get




substitute the values in the above equation, we get




To estimate the volume of cylinder,
= (π
/4) h
Here, π = 3.14 and d = 1.6 cm
Height of the cylinder, h = t = 2 cm
substitute the values in the above equation, we get
![$V_c=[3.14 (1.6) / 4] (2)](https://tex.z-dn.net/?f=%24V_c%3D%5B3.14%20%281.6%29%20%2F%204%5D%20%282%29)
![$V_c=[3.14 (2.56) / 4] (2)](https://tex.z-dn.net/?f=%24V_c%3D%5B3.14%20%282.56%29%20%2F%204%5D%20%282%29)


Substitute the values in the equation, we get




Therefore, the volume of metal in the hex nut, to the nearest tenth exists
.
To learn more about volume of cylinder and prism refer to:
brainly.com/question/12669337
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