What is the volume of a right hexagonal pyramid with base edge of 1 cm and height of 2cm
Would I use V=BH 6(2)=12cm^3
To calculate the volume of a right hexagonal pyramid, you can indeed use the formula V = BH, where B represents the base area and H represents the height of the pyramid.
The first step is to calculate the base area B.
For a right hexagonal pyramid, the base is a regular hexagon. Since the base edge is given as 1 cm, you can calculate the area of a regular hexagon using the formula:
B = 3 × √3 × s^2 / 2
In this case, s represents the length of one side of the hexagon, which is the same as the base edge of the pyramid. Therefore, s = 1 cm.
Plugging in the values, you get:
B = 3 × √3 × 1^2 / 2
B = 3 × √3 / 2
Now that you have the base area B, you can calculate the volume V by multiplying B by the height H. In this case, the height is given as 2 cm:
V = B × H
V = (3 × √3 / 2) × 2
V = 3 × √3
So, the volume of the right hexagonal pyramid with a base edge of 1 cm and a height of 2 cm is 3 × √3 cm³.
The general formula for a pyramid
= (1/3) base area x height
Your base is a hexagon with sides of 1.
You can split the hexagon into 6 equilateral triangles.
Find the area of one of those first:
(use the ratio of the 30-60-90 triangle to find the height to be √3/2)
Area of one triangle = (1/2)(1)√3/2) = √3/4
so 6 of them would be 6√3/4 or 3√3/2
volume of your pyramid
= (1/3)(1)(3√3/2)
= 3√3/6