Question

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?

Answer 1

• 26 : 27

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