The volume of the pyramid is 250, the height of this and the truncated pyramid is 5: 3. Find the volume of the truncated pyramid.

Pyramid volume:

V = 1/3 * S * h, where V is the volume of the pyramid (V = 250), S is the area of the base, h is the height of the pyramid (h = 5x).

V = 1/3 * S * 5x.

The volume of the truncated pyramid (the height of the truncated pyramid is equal to the difference between the heights of the full pyramid and the truncated one (h1 = 2x)):

S1 / S2 = (5x / (5x – 2x)) ^ 2 = 2.78.

S2 = S1 / 2.78.

V1 = 1/3 * h1 * (S1 + √ (S1 * S2) + S2) = 1/3 * 2x * (S + √ (S * S / 2.78) + S / 2.78) = 1 / 3 * 2x * 1.96S = 1.31xS.

V / V1 = 1/3 * S * 5x / 1.31xS = 1.27.

V1 = V / 1.27 = 250 / 1.27 = 196.85.