(a)
To find: The volume of cube.
(a)
Answer to Problem 1CE
The volume of each cube is equal to
Explanation of Solution
Given information:
The diagonal of a cube intersect to divide the cube into six congruent pyramids as shown. The base of each pyramid is a face of the cube, and height of each pyramid is
Calculation:
The edge length of cube is equal to
It is given that it is divided into six congruent pyramids. All of the six pyramids are similar to each other. So,
Therefore, the volume of each cube is equal to
(b)
To prove: The volume of pyramid is
(b)
Explanation of Solution
Given information:
The diagonal of a cube intersect to divide the cube into six congruent pyramids as shown. The base of each pyramid is a face of the cube, and height of each pyramid is
Proof:
The base of each pyramid is
From part (a), the volume of a pyramid is
Now, calculate the volume of pyramid in terms of base area as:
Hence, it is proved that the volume of the pyramid is
Chapter 12 Solutions
McDougal Littell Jurgensen Geometry: Student Edition Geometry
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