A regular hexagonal pyramid whose base perimeter is 60cm has an altitude of 30cm. The volume of the pyramid is??

The volume of any "pointy thing" is

(1/3) base x height

our base is a hexagon where each side is 60/6 or 10 cm
of course we have 6 equilateral triangles
the area of one of these is
(1/2)(10)(10)sin60° = 50√3/2 = 25√3
and we have 6 of them, so the area of the base is
150√3

Volume = (1/3)(150√3)(30) = 1500√3 cm^3

To find the volume of a regular hexagonal pyramid, you can use the formula:

Volume = (1/3) * Base Area * Height

First, let's find the base area of the regular hexagon.

Since the perimeter of the hexagon is given as 60 cm, we know that the length of one side of the hexagon is 60 cm divided by 6 sides, which gives us 10 cm.

To find the area of a regular hexagon, we can use the formula:

Area = (3 * sqrt(3) * s^2) / 2

Where "s" is the length of one side.

Substituting in the value we found for "s" as 10 cm:

Area = (3 * sqrt(3) * 10^2) / 2
= (3 * sqrt(3) * 100) / 2
= (300 * sqrt(3)) / 2
= 150 * sqrt(3) cm^2

Now, substitute the values we have into the volume formula:

Volume = (1/3) * Base Area * Height
= (1/3) * (150 * sqrt(3)) * 30
= (1/3) * 150 * 30 * sqrt(3)
= 150 * 10 * sqrt(3)
= 1500 * sqrt(3) cm^3

So, the volume of the regular hexagonal pyramid is 1500 * sqrt(3) cm^3.

To find the volume of a regular hexagonal pyramid, you can use the formula:

Volume = (1/3) * Base Area * Height

First, let's find the base area of the pyramid.

The regular hexagon on the base has a perimeter of 60 cm, which means that each side's length is 60 cm divided by 6 (since a hexagon has 6 sides).

Perimeter of the hexagon = 60 cm
Length of each side = 60 cm / 6 = 10 cm

Next, let's find the apothem of the hexagon, which is the distance from the center of the hexagon to any of its sides.

The apothem of a regular hexagon can be found using the formula:

Apothem = (Side Length) / (2 * tan(π/6))

Where tan(π/6) is the tangent of 30 degrees (π/6 radians), which is approximately 0.577.

Apothem = 10 cm / (2 * 0.577)
≈ 8.6603 cm

Now, we can find the area of the base of the pyramid using the formula:

Base Area = (3 * √3 * Apothem^2) / 2

Base Area = (3 * √3 * 8.6603 cm^2) / 2
≈ 78.5918 cm^2

Finally, we can calculate the volume of the pyramid using the formula:

Volume = (1/3) * Base Area * Height

Volume = (1/3) * 78.5918 cm^2 * 30 cm
≈ 785.918 cm^3

Therefore, the volume of the regular hexagonal pyramid is approximately 785.918 cm^3.