The base of the right pyramid is a rectangle of length 80 cm and width 60 cm. Each slant edge of the pyramid is 130 cm. Calculate the volume of the pyramid.

To calculate the volume of a pyramid, we use the formula:

Volume = (1/3) * base area * height

First, we need to find the height of the pyramid. We can do this by using the Pythagorean theorem on the right triangle formed by the slant edge, height, and half of the base.

Let h be the height of the pyramid, then we have:

h^2 + (40)^2 = (130)^2
h^2 + 1600 = 16900
h^2 = 15300
h = √15300
h ≈ 123.69 cm

Now, we can calculate the volume of the pyramid:

Volume = (1/3) * 80 * 60 * 123.69
Volume = (1/3) * 4800 * 123.69
Volume = 1600 * 123.69
Volume ≈ 198,704.8 cm^3

Therefore, the volume of the pyramid is approximately 198,704.8 cm^3.

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
- h is the height of the pyramid

In this case, the base of the pyramid is a rectangle, so the area of the base is:

```
B = l - w = 80 cm - 60 cm = 4800 cm^2
```

The height of the pyramid is equal to the slant height, which is given as 130 cm.

Therefore, the volume of the pyramid is:

```
V = (1/3) - 4800 cm^2 - 130 cm = 2,080,000 cm^3
```

Therefore, the volume of the pyramid is 2,080,000 cm^3.

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