Concept explainers
To find:The ratios of base circumferences, scale factor, lateral areas, total areas and volumes of two similar cones.
Answer to Problem 9CE
The two similar cones scale factoris
Explanation of Solution
Given information:
The ratio of slant heights of two similar cones is
Calculation:
The ratio of the corresponding sides of any two similar geometric figures is termed as Scale factor.The theorem of similar
(i) The ratio of base areas, lateral areas and total areas is
(ii) The ratio of base circumferences is
(iii) The ratio of their volumes is
Let the two slant heights of cones be
Expression to find the scale factor from the above theorem is:
Substitute
Therefore, the ratio of scale factor of two similar cones is
Expression to find the base circumferences from the above theorem is:
Substitute
Therefore, the ratio of base circumferences of two similar cones is
Expression to determine the lateral area of two similar cones from the similar solids theorem is:
Substitute
Therefore, the ratios of lateral areas of two similar conesis
Expression to determine the total area of two similar cones from the above theorem is:
Substitute
Therefore, the ratios of total areas of two similar conesis
Expression to determine the volumes of two similar cones from the above theorem is:
Substitute
So, the ratios of volumes of two similar conesis
Therefore,the two similar cones scale factor ratio is
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