The volume of a frustum of a pyramid having an upper base area of 1000 m² and of lower base of 64 m² is 4066 m³. Find the altitude of the frustum of the Pyramid

To find the altitude of the frustum of the pyramid, we can use the formula for the volume of a frustum of a pyramid:

V = (1/3) * h * (A1 + A2 + sqrt(A1 * A2))

Where:
V is the volume of the frustum,
h is the altitude of the frustum,
A1 is the area of the upper base, and
A2 is the area of the lower base.

Given:
A1 = 1000 m²,
A2 = 64 m², and
V = 4066 m³.

Let's plug these values into the formula and solve for h:

4066 = (1/3) * h * (1000 + 64 + sqrt(1000 * 64))

Simplifying the equation:

12198 = h * (1064 + sqrt(64000))

Now, let's solve for h:

h = 12198 / (1064 + sqrt(64000))

Using a calculator:

h ≈ 6.52 m

Therefore, the altitude of the frustum of the pyramid is approximately 6.52 meters.

To find the altitude of the frustum of the pyramid, we can use the formula for the volume of a frustum of a pyramid:

V = (1/3) * h * (A1 + A2 + sqrt(A1 * A2))

Where:
V is the volume of the frustum,
h is the altitude of the frustum,
A1 is the area of the upper base, and
A2 is the area of the lower base.

Given:
A1 = 1000 m²,
A2 = 64 m²,
V = 4066 m³.

We can rearrange the formula to solve for h:

h = (3V) / (A1 + A2 + sqrt(A1 * A2))

Now, substitute the given values into the formula:

h = (3 * 4066) / (1000 + 64 + sqrt(1000 * 64))

To calculate the square root term, multiply the two base areas and then find the square root:

sqrt(1000 * 64) = sqrt(64000) ≈ 253.54

Now substitute this value back into the equation:

h = (3 * 4066) / (1000 + 64 + 253.54)

h = 12198 / 1317.54

h ≈ 9.27 m

Therefore, the altitude of the frustum of the pyramid is approximately 9.27 meters.

since the areas of the cut-off part and the entire pyramid is 64/100, the heights are in the ratio 8:10 = 4/5

That means that the cut-off part has height 1/5 that of the whole pyramid.
Now you can use that to find the height desired.