(a)
To find:The ratios of the heights of two similar pyramids.
(a)
Answer to Problem 8WE
The ratios of the heights of two similar pyramidsis
Explanation of Solution
Given information:
The volumes of two similar pyramids are 3 and 375.
Calculation:
The ratio of the corresponding sides of any two similar geometric figures is termed as Scale factor.
Let the two volumes of pyramids be
The theorem of similar
Expression to determine the volumes of two similar pyramids from the above theorem is:
Substitute
To determine the ratio of heights, apply cube root at both sides in the above expression.
Therefore, the ratios of heights of two similar pyramids is
(b)
To find:The ratios of base areas of two similar pyramids.
(b)
Answer to Problem 8WE
The ratios of base areas of two similar pyramids is
Explanation of Solution
Given information:
The volumes 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 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
(c).
To find:The ratios of total areas of two similar pyramids.
(c).
Answer to Problem 8WE
The ratios of total areas of two similar pyramids is
Explanation of Solution
Given information:
The volumes of two similar pyramids are
Calculation:
As calculated in part (a), the value of
Expression to determine the total areas of two similar pyramids from the above theorem is:
Substitute
Therefore, the ratios of total areas 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