Question

a regular hexagonal nut of side 1 cm and length 3 cm with a central hole of diameter 1 cm. 3 cm 1 cm 1 cm. Calculate the volume of metal in the nut. (Ignore the thread and give your answer correct to 3 significant figures.) (WAEC]​

Answer 1

Answer:

  5.44 cm³

Step-by-step explanation:

The volume of the hexagonal nut can be found by multiplying the area of the end face by the length of the nut. The end face area is the difference between the area of the hexagon and the area of the hole.

The area of a hexagon with side length s is given by ...

  A = (3/2)√3·s²

For s=1 cm, the area is ...

  A = (3/2)√3(1 cm)² = (3/2)√3 cm²

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The area of a circle is given by ...

  A = πr²

The radius of a circle with diameter 1 cm is 0.5 cm. Then the area of the hole is ...

  A = π(0.5 cm)² = 0.25π cm²

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The volume is the face area multiplied by the length, so is ...

  V = Bh = ((3/2)√3 -0.25π)(3) . . . . . cm³

  V = (9/2)√3 -0.75π cm³ ≈ 5.44 cm³

The volume of the metal is about 5.44 cm³.