Question

A regular hexagonal prism has sides of 4 cm for the hexagonal bases and is 10 cm in height. Find its exact

volume. Then, quickly find the exact volume of a regular hexagonal pyramid inscribed in the prism. If you

don’t have a 3 in your answers, something’s gone wrong.

Answer 1

Exact volume of the hexagonal prism = 240√3 cm³

Exact volume of the hexagonal pyramid = 80√3 cm³

Step by step explanation:

Volume of hexagonal prism = [(3√3)/2]×a²h

Where a = base edge

h = height

From the question,

a = 4cm, h = 10cm

V = [(3√3)/2]×(4)²×(10)

V = (3√3) × 160/2

V = 240√3 cm³

Exact volume of the hexagonal prism = 240√3 cm³

Volume of hexagonal pyramid = [(√3)/2]×a²h

a = 4cm, h = 10cm

V = [(√3)/2]×(4)²×(10)

V = (√3) × 160/2

V = 80√3 cm³

Exact volume of the hexagonal pyramid = 80√3 cm³