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A frustum of height 4 is part of a larger pyramid of height 6. What is the ratio of the volume of the frustum to the volume of the pyramid?

Respuesta :

mhanifa

Answer:

  • 26 : 27

Step-by-step explanation:

The volume of the pyramid with height of 6:

  • V = 1/3bh = 1/3b*6 = 2b,
  • b is area of the base

The volume of the smaller pyramid is:

  • V₁ = 1/3*b₁h₁

We know:

  • h₁ = 6 - 4 = 2
  • h₁/h = 2/6 = 1/3

The base sides have same ratio as similar triangles.

  • b₁ = (1/3)²b= b/9

The volume of smaller pyramid:

  • V₁ = 1/3*2*b/9 = 2b/27

The difference of the volumes is the volume of the frustum:

  • V₂ = V - V₁
  • V₂ = 2b - 2b/27 = 52b/27

The ratio of V₂ to V is:

  • 52b/27 ÷ 2b =
  • 26/27

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