A pyramid of volume 344 square units is sliced into two pieces by a plane parallel to the base of the pyramid and 10 units away from the plane of the base. The volume of the resulting frustum is 301 square units. What was the height of the original pyramid?

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Mathematics

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7 April, 06:12

A pyramid of volume 344 square units is sliced into two pieces by a plane parallel to the base of the pyramid and 10 units away from the plane of the base. The volume of the resulting frustum is 301 square units. What was the height of the original pyramid?

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Daniella Crawford · Answer 1

80 units

Step-by-step explanation:

v = 1/3 bh

v₁ = 1/3 * b * h₁ = 344

v₂ = 1/3 * b * h₂ = 301

v₁ / v₂ = h₁ / h₂ = 344 / 301

h₂ = h₁ - 10

h₁ / (h₁ - 10) = 344 / 301

344 * (h₁ - 10) = 301 * h₁

344 * h₁ - 3440 = 301 * h₁

43 * h₁ = 3440

h₁ = 80