The volume of the truncated pyramid is 183 cm³, the area of the lower base is 25 cm²

The volume of the truncated pyramid is 183 cm³, the area of the lower base is 25 cm², the area of the upper base is 16 cm². Find the height of the frustum.

The volume of the truncated pyramid is determined by the formula: V = (1/3) * h * (S1 + S2 + √S1 * √S2), where h is the height of the truncated pyramid, S1, S2 are the areas of the upper and lower bases. From here we can find h: h = 3V / (S1 + S2 + √S1 * √S2) = 3 * 183 / (16 + 25 + √25 * √16) = 3 * 183 / (16 + 25 + 4 * 5) = 3 * 183/61 = 9 cm.