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 in Figure 15.28, we can use the formula for the volume of a frustum of a pyramid. The frustum is the portion of the pyramid between the top and bottom, created by removing the top section.

The formula for the volume of a frustum of a pyramid is:

V = (1/3) * h * (A + sqrt(A * B) + B)

Where:

V = Volume of the frustum

h = Height of the frustum (vertical distance between the top and bottom)

A = Area of the top base

B = Area of the bottom base

Given the dimensions provided, we can calculate the areas of the bases:

Area of the top base (A) = 4 m * 4 m = 16 m²

Area of the bottom base (B) = 20 m * 20 m = 400 m²

The height of the frustum (h) is given as 12 m.

Now we can plug these values into the formula:

V = (1/3) * 12 m * (16 m² + sqrt(16 m² * 400 m²) + 400 m²)

Calculating the square root and simplifying:

V = (1/3) * 12 m * (16 m² + 20 m² + 400 m²)

V = (1/3) * 12 m * (436 m²)

V = 1744 m³

Therefore, the estimated original volume of the pyramid in Figure 15.28 is approximately 1744 cubic meters.