Question

What is the volume of the regular pyramid?A) 4492.8 cm^3B) 13,478.4 cm^3C) 6739.4 cm^3D) 8985.6 cm^3

Answer 1

The area of a regular pyramid is:

`Ap=(1)/(3)(Ab\cdot h)`

Where:

Ap = Area of the regular pyramid

Ab = Area of the basis

h = height of the pyramid

And, Ab is:

`Ab=(n)/(2)\cdot(s\cdot a)`

Where:

n = number of sides of the polygon

s = measure of the side of the polygon

a = apothem

So, to solve this question, follow the steps below.

Step 01: Find Ab.

To find Ab, let's extract the info from the problem:

n = 6

s = 12 cm.

a = 10.4 cm.

Then,

`\begin{gathered} Ab=(6)/(2)\cdot(12\cdot10.4) \\ Ab=3\cdot(124.8) \\ Ab=374.4cm^2 \end{gathered}`

Step 02: Use Ab to find Ap.

From the problem:

h = 36 cm.

Then,

`\begin{gathered} Ap=(1)/(3)(374.4\cdot36) \\ Ap=4492.8cm^3 \end{gathered}`

Answer: A) 4492.8 cm³.