Question

find the volume of this square based pyramid.
? \\(\text{in}^3\\)

Explanation:

Identify the given dimensions

The pyramid has a square base with a side length \(s = 12\text{ in}\) and a vertical height \(h = 10\text{ in}\).

Calculate the base area

The base is a square, so its area \(B\) is calculated by squaring the side length:

$$B = s^2 = 12^2 = 144\text{ in}^2$$

Apply the pyramid volume formula

The volume \(V\) of a pyramid is given by:

$$V = \frac{1}{3} \cdot B \cdot h$$

Compute the final volume

Substitute the base area \(B = 144\text{ in}^2\) and height \(h = 10\text{ in}\) into the formula:

$$V = \frac{1}{3} \cdot 144 \cdot 10 = 48 \cdot 10 = 480\text{ in}^3$$

Answer:

Find the volume of this square based pyramid.

<blank>480</blank> \(\text{in}^3\)