(a)
To find:The ratios of lengths of Earth and moon equators.
(a)
Answer to Problem 5WE
The ratios of equators length of Earth and moon is
Explanation of Solution
Given information:
The diameter of Earth is
Calculation:
The ratio of the corresponding sides of any two similar geometric figures is termed as Scale factor. Let, the diameters of Earth and moon be
The length of the equator of earth and moon is equal to diameter of the Earth and moon.
To find the equators lengths, write the corresponding diameter in the ratio equating to length ratio.
Substitute
Therefore, the equators length ratios of Earth and moon is
(b)
To find:The ratios of areas of Earth and Moon.
(b)
Answer to Problem 5WE
The ratios of areas of Earth and Moon is
Explanation of Solution
Given information:
The diameter of Earth is
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 Earth and moon from the above theorem is:
Substitute
Therefore, the ratios of areas of Earth and Moon is
(c)
To find:The ratios of volumes ofEarth and Moon.
(c)
Answer to Problem 5WE
The ratios of volumes of Earth and Moon is
Explanation of Solution
Given information:
The diameter of Earth is
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 ratio of volumes of Earth and moon from the above theorem is:
Substitute
Therefore, the ratios of volumes of Earth and Moon is
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