How to find the volume and height of the pyramid?

To find the volume and height of a pyramid, you will need to know the dimensions of the base and the slant height of the pyramid.

1. Calculate the volume of the pyramid using the formula:
Volume = (1/3) * base area * height
where base area is the area of the base of the pyramid and height is the height of the pyramid.

2. To find the height of the pyramid, you can use the formula:
height = (Volume * 3) / base area

3. If you know the slant height of the pyramid, you can also use the Pythagorean theorem to find the height:
height = sqrt(slant height^2 - (base side/2)^2)

By using these formulas, you can find both the volume and height of a pyramid.

Volume:

The volume of a pyramid is given by the formula:

```
V = (1/3) - B - h
```

where:

- V is the volume of the pyramid
- B is the area of the base of the pyramid
- h is the height of the pyramid

Height:

If you know the volume and the area of the base, you can find the height using the formula:

```
h = 3 - V / B
```

Example:

Let's say you have a rectangular pyramid with a base of length 10 cm and width 8 cm, and a height of 12 cm.

Volume:

```
V = (1/3) - (10 cm - 8 cm) - 12 cm
V = 320 cm³
```

Height:

If you know the volume and the area of the base, you can find the height using the formula:

```
h = 3 - V / B
h = 3 - 320 cm³ / (10 cm - 8 cm)
h = 12 cm
```

Therefore, the volume of the rectangular pyramid is 320 cm³ and the height is 12 cm.