(a)
To check: The pyramid with greater volume.
(a)
Answer to Problem 32WE
Both the pyramids have equal volume.
Explanation of Solution
Given information:
Different pyramids are inscribed in two identical cubes, as shown below:
The formula for the volume of pyramids is one third of product of base area and height.
The base of both the pyramids is of same dimensions. So, the base area for both the pyramids is equal. The height of both the pyramids is also the same. Both the base area and height of pyramids are equal.
Therefore, both the pyramids have equal volume.
(b)
To check: The pyramid that has the greater total area.
(b)
Answer to Problem 32WE
The total area of pyramid
Explanation of Solution
Given information:
Different pyramids are inscribed in two identical cubes, as shown below:
The total area of pyramid is the sum of lateral area and area of base. The area of base for both the pyramids is same.
The lateral area of first pyramid is the sum of the area of
The area of triangle
The area of triangle
So, the area of triangles
The height of triangle
So, The area of triangle
So, the area of triangles
Simplify the lateral area of first pyramid.
The formula for the lateral area of second pyramid is equal to
Simplify the slant height of the pyramid:
Substitute
The lateral area of first pyramid is greater than the lateral area of second pyramid.
Therefore, the total area of pyramid
Chapter 12 Solutions
McDougal Littell Jurgensen Geometry: Student Edition Geometry
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