If the radius of a sphere is doubled, what is the ratio of the volume of the first sphere to that of the second sphere?
Answers
Given : Radius of a sphere is doubled.
Let 'r' be the radius of the first sphere.
& the radius of the second sphere be '2r'
Volume of a sphere = (4/3)πr³
Ratio of the volume of the first sphere (V1) to that of the second sphere (V2) = (4/3)πr³/(4/3)π(2r)³
V1/V2 = r³/(2r)³
V1/V2 = ⅛
V1 : V2 = 1 : 8
Hence, the ratio of the volume of the first sphere to that of the second sphere is 1 : 8.
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Step-by-step explanation:
Given : Radius of a sphere is doubled.
Let 'r' be the radius of the first sphere.
& the radius of the second sphere be '2r'
Volume of a sphere = (4/3)πr³
Ratio of the volume of the first sphere (V1) to that of the second sphere (V2) = (4/3)πr³/(4/3)π(2r)³
V1/V2 = r³/(2r)³
V1/V2 = ⅛
V1 : V2 = 1 : 8