(a)
To find:The ratio of the areas of two spheres.
(a)
Answer to Problem 4CE
The ratio of the areas of two spheres is
Explanation of Solution
Given information:The diameters of spheres are
Calculation:
Spheres are always similar and the scale factor of these spheres is equal to the ratio of the diameters. So, the scale factor of both spheres is:
The ratio of the areas of the spheres is:
Therefore, the ratio of the areas of both the spheres is
(b)
To find:The ratio of the volumes of two spheres.
(b)
Answer to Problem 4CE
The ratio of the volumes of both the spheres is
Explanation of Solution
Given information:Two spheres have diameters
Calculation:
Spheres are always similar and the scale factor of these spheres is equal to the ratio of the diameters. So, the scale factor of both spheres is:
The ratio of the volumes of the spheres is:
Therefore, the ratio of the volumes of both the spheres is
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