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Answer:
Step-by-step explanation:
Part a: The radius of the second sphere is 5 inches.
Part b: The volume of the second sphere is 523.33 in³
Part c; The radius of the third sphere is 1.875 inches.
Part d: The volume of the third sphere is 27.59 in³
Explanation:
Given that the radius of the sphere is 2.5 inches.
Part a: We need to determine the radius of the second sphere.
Given that the second sphere has twice the radius of the given sphere.
Radius of the second sphere = 2 × 2.5 = 5 inches
Thus, the radius of the second sphere is 5 inches.
Part b: we need to determine the volume of the second sphere.
The formula to find the volume of the sphere is given by
Substituting and
, we get,
Rounding off to two decimal places, we have,
Thus, the volume of the second sphere is 523.33 in³
Part c: We need to determine the radius of the third sphere
Given that the third sphere has a diameter that is three-fourths of the diameter of the given sphere.
Hence, we have,
Diameter of the third sphere =
Radius of the third sphere =
Thus, the radius of the third sphere is 1.875 inches
Part d: We need to determine the volume of the third sphere
The formula to find the volume of the sphere is given by
Substituting and
, we get,
Rounding off to two decimal places, we have,
Thus, the volume of the third sphere is 27.59 in³