(a).
To find:The ratios of volumes of two similar sphere.
(a).
Answer to Problem 5CE
The ratios of volumes of two similar sphere is
Explanation of Solution
Given information:
The volumes of two similar spheres are
Calculation:
Let, the two volumes be
Expression of given two volumes of similar spheres in ratio is:
To find the ratio of volumes, divide the numerator and denominator of the above expression by
Therefore, the volume ratio of two similar spheres in reduced form is
(b).
To find:The ratios of diameters of two similar sphere.
(b).
Answer to Problem 5CE
The ratios of diameters of two similar sphere is
Explanation of Solution
Given information:
The volumes of two similar spheres are
Calculation:
The ratio of the corresponding sides of any two similar geometric figures is termed as Scale factor. Let, the diameters of sphere be
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 diameters from volumes of spheresusing the above theorem is:
Substitute
To determine the ratio of diameters, apply cube root at both sides in the above expression.
Therefore, the ratio of diameter of two similar sphere is
(c).
To find:The ratios of areas of two similar spheres.
(c).
Answer to Problem 5CE
The ratios of areas of two similar spheres is
Explanation of Solution
Given information:
The volumes of two similar spheres are
Calculation:
As calculated in part(b), The value of
The theorem of similar solids states that if the scale factor of two similar solids is
Expression to determine theratio of area of spheresfrom the above theorem is:
Substitute
Therefore, the ratios of areas of two similar spheres is
Chapter 12 Solutions
McDougal Littell Jurgensen Geometry: Student Edition Geometry
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