(a).
To find:The ratios of the radii of two similar cones.
(a).
Answer to Problem 7WE
The ratios of the radii of two similar conesis
Explanation of Solution
Given information:
The volumes of two similar cones are
Calculation:
The ratio of the corresponding sides of any two similar geometric figures is termed as Scale factor.
Let the two Volumes of cones be
The theorem of similar solids states that if the scale factor of two similar solids is
Expression to determine the volumes of two similar cones from the above theorem is:
Substitute
To determine the ratio of their radii, apply cube root at both sides in the above expression.
Therefore, the ratios of radii of two similar cones is
(b).
To find:The ratios of slant heights of two similar cones.
(b).
Answer to Problem 7WE
The ratios of slant heights of two similar conesis
Explanation of Solution
Given information:
The volumes of two similar cones are
Calculation:
The theorem of similar
Let the two Volumes of cones be
The theorem of similar solids states that if the scale factor of two similar solids is
Expression to determine the volumes of two similar cones from the above theorem is:
Substitute
To determine the ratio of their slant heights, apply cube root at both sides in the above expression.
Therefore, the ratios of the slant heights of two similar cones is
(c).
To find:The ratios of the lateral areas of two similar cones.
(c).
Answer to Problem 7WE
The ratios of lateral areas of two similar conesis
Explanation of Solution
Given information:
The volumes of two similar cones 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 cones from the above theorem is:
Substitute
Therefore, the ratios of the lateral areas of two similar cones 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