Question

Pyramid A has a triangular base where each side measures 4 units and a volume of 36 cubic units. Pyramid B has the same height, but each side of its base is 6 units long.

Answer 1

81

Explanation:

Answer 2

The volume of pyramid B is 81 cubic units

Explanation:

Given

Pyramid A

-- base sides

-- Volume

Pyramid B

--- base sides

Required

Determine the volume of pyramid B [Missing from the question]

From the question, we understand that both pyramids are equilateral triangular pyramids.

The volume is calculated as:

Where B represents the area of the base equilateral triangle, and it is calculated as:

Where s represents the side lengths

First, we calculate the height of pyramid A

For Pyramid A, the base area is:

The height is calculated from:

This gives:

Make h the subject

To calculate the volume of pyramid B, we make use of:

Since the heights of both pyramids are the same, we can make use of:

The base area B, is then calculated as:

Where

So:

So:

Where

and