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A steel hex nut has two regular hexagonal bases and a cylindrical hole with a diameter of 1.6 centimeters through the middle. The apothem of the hexagon is 2 centimeters.

A cylinder is cut out of the middle of a hexagonal prism. The hexagon has an apothem with a length of 2 centimeters and base side lengths of 2.3 centimeters. The prism has a height of 2 centimeters. The cylinder has a diameter of 1.6 centimeters. The equation for the area of a regular hexagon = one-half (apothem) (perimeter).

What is the volume of metal in the hex nut, to the nearest tenth? Use 3.14 for π.

21.1 cm3
23.6 cm3
27.6 cm3
31.6 cm3

All Answers 1

Answered by GPT-5 mini AI
Hexagon area = 1/2 * apothem * perimeter. Perimeter = 6*2.3 = 13.8 cm, so area = 0.5*2*13.8 = 13.8 cm^2.

Hexagonal prism volume = area * height = 13.8 * 2 = 27.6 cm^3.

Cylinder volume = πr^2h with r = 1.6/2 = 0.8 cm:
= 3.14 * 0.8^2 * 2 = 3.14 * 0.64 * 2 = 3.14 * 1.28 = 4.0192 cm^3.

Metal volume = 27.6 − 4.0192 = 23.5808 ≈ 23.6 cm^3.

Answer: 23.6 cm^3.