(a)
To find:The ratios of base areas of two similar pyramids.
(a)
Answer to Problem 4WE
The ratios of base areas of two similar pyramids is
Explanation of Solution
Given information:
The heights of two similar pyramids are
Calculation:
The ratio of the corresponding sides of any two similar geometric figures is termed as scale factor.
Let the two heights of pyramids be
To find the scale factor, write the corresponding heights in the ratio equating to scale factor.
Substitute
Therefore, from the above expression the value of
The theorem of similar solids states that if the scale factor of two similar solids is
Expression to determine the area of two similar pyramids from the above theorem is:
To find the value of
Therefore, the ratios of base areas of two similar pyramids is
(b).
To find:The ratios of lateral areas of two similar pyramids.
(b).
Answer to Problem 4WE
The ratios of lateral areas of two similar pyramids is
Explanation of Solution
Given information:
The heights of two similar pyramids are
Calculation:
As calculated in part(a), the value of
The theorem of similar solids states that if the scale factor of two similar solids is
Expression to determine the lateral area of two similar pyramids from the above theorem is:
Substitute
Therefore, the ratios of lateral areas of two similar pyramids is
(c).
To find:The ratios of total areas of two similar pyramids.
(c).
Answer to Problem 4WE
The ratios of total areas of two similar pyramids is
Explanation of Solution
Given information:
The heights of two similar pyramids are
Calculation:
As calculated in part(a), the value of
The theorem of similar solids states that if the scale factor of two similar solids is
Expression to determine the total area of two similar pyramids from the above theorem is:
Substitute
Therefore, the ratios of total areas of two similar pyramids is
(d).
To find:The ratios of volumes of two similar pyramids.
(d).
Answer to Problem 4WE
The ratios of volumes of two similar pyramids is
Explanation of Solution
Given information:
The heights of two similar pyramids are
Calculation:
As calculated in part(a), the value of
The theorem of similar solids states that if the scale factor of two similar solids is
Expression to determine the volumes of two similar pyramids from the above theorem is:
Substitute
Therefore, the ratios of volumes of two similar pyramids is
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- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage Learning