Question

a regular hexagonal pyramid is 20m high.side of the base is 5m.find the volume and the slant height of the pyramid

Answer 1

20 multiply by 5 for volume finding 100

Answer 2

The volume of the regular hexagonal pyramid is 433 m³ and the slant height of the pyramid is 20.46 m.

Step-by-step explanation:

The height of the regular hexagonal pyramid, h = 20 m

The side of the base, a = 5 m

Case 1: Finding the volume of the pyramid

The area of the hexagonal base of the pyramid = $\frac{3\sqrt{3}}{2} * a^2 = \frac{3\sqrt{3}}{2} * 5^2$= 64.95 m²

We know that,

The volume of the pyramid is given by,

V = $\frac{1}{3}$ * area of base * height

Substituting the value of area and height in the formula, we get

V = $\frac{1}{3}$ * 64.95 * 20 = 433 m³

Thus, the volume of the pyramid is 433 m³

Case 2: Finding the slant height of the pyramid

Referring to the figure attached below, we have

O → vertex of the pyramid

G → centre of the hexagonal base

OG → axis or height of the hexagonal pyramid

H → midpoint of side AB

OH → slant height of the pyramid

∆ OGH → right-angled triangle

Let’s consider ∆ AGB,

GH is the altitude

So, GH = (√3/2) * a = (√3/2) * 5 = 4.33 m

In ∆ OGH, applying the Pythagoras theorem, we get

OH = √[GH² + OG²]

⇒ OH = √[(4.33)² + (20)²]

⇒ OH = √417.74

⇒ OH = 20.46 m

Thus, the slant height of the pyramid is 20.46 m.

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