Question

estimate the original volume of the pyramid in fig 15.28 given that it's frustum has a 4 m by 4 m squared top which is 12 m vertically above the square base which is 20 m by 20 m (assume that the original problem was raised to a point . Neglect the volume of the entrance of the right of the photograph)​

Answer 1

Explanation:

To estimate the original volume of the pyramid, we can use the formula for the volume of a frustum of a pyramid:

V = (1/3)h(a^2 + ab + b^2)

Where V is the volume, h is the height of the frustum, a is the side length of the top square, and b is the side length of the bottom square.

In this case, the top square has a side length of 4 m, and the bottom square has a side length of 20 m. The height of the frustum is 12 m.

Plugging these values into the formula, we get:

V = (1/3) * 12 * (4^2 + 4*20 + 20^2)

Simplifying the equation:

V = (1/3) * 12 * (16 + 80 + 400)

V = (1/3) * 12 * 496

V = 12 * 496/3

V = 1984

Therefore, the estimated original volume of the pyramid is 1984 cubic meters.