Question
The volume of a cone is 25/3 * pi*c * m ^ 3 What is the volume of a sphere if its radius is the same as the cone's and the height of the cone is equal to the sphere's diameter? (1 point)
25/6 * pi*c * m ^ 3
25pi*c * m ^ 3
25/2 * pi*c * m ^ 3
50/3 * pi*cm * g ^ 3
25/6 * pi*c * m ^ 3
25pi*c * m ^ 3
25/2 * pi*c * m ^ 3
50/3 * pi*cm * g ^ 3
Answers
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Answered by
GPT 3.5
The volume of a cone = (1/3) * pi * r^2 * h = 25/3 * pi * c * m^3
Since the radius of the sphere is equal to the radius of the cone and the height of the cone is equal to the diameter of the sphere, the radius of the sphere = c and the height of the cone = 2c.
The volume of the sphere = (4/3) * pi * r^3 = (4/3) * pi * c^3
Therefore, the volume of the sphere, when simplified, will be:
(4/3) * pi * c^3 = (4/3) * pi * c * c^2 = 4/3 * pi * c * c^2 = 4 * pi * c^3 / 3
= 25 /3 * pi* c * m^3
Therefore, the correct answer is:
25 / 3 * pi * c * m^3
Since the radius of the sphere is equal to the radius of the cone and the height of the cone is equal to the diameter of the sphere, the radius of the sphere = c and the height of the cone = 2c.
The volume of the sphere = (4/3) * pi * r^3 = (4/3) * pi * c^3
Therefore, the volume of the sphere, when simplified, will be:
(4/3) * pi * c^3 = (4/3) * pi * c * c^2 = 4/3 * pi * c * c^2 = 4 * pi * c^3 / 3
= 25 /3 * pi* c * m^3
Therefore, the correct answer is:
25 / 3 * pi * c * m^3
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