When the radius of a sphere is doubled, what is the resulting change in volume?ResponsesA The original volume is doubled.The original volume is doubled.B The original volume is multiplied by 4.The original volume is multiplied by 4.C The original volume is multiplied by 8.The original volume is multiplied by 8.D The original volume is multiplied by 10.
Question
When the radius of a sphere is doubled, what is the resulting change in volume?ResponsesA The original volume is doubled.The original volume is doubled.B The original volume is multiplied by 4.The original volume is multiplied by 4.C The original volume is multiplied by 8.The original volume is multiplied by 8.D The original volume is multiplied by 10.
Solution
The volume of a sphere is given by the formula V = 4/3πr³. If the radius is doubled, the new volume V' is given by V' = 4/3π(2r)³ = 4/3π8r³ = 8V. Therefore, the original volume is multiplied by 8. So, the correct answer is C. The original volume is multiplied by 8.
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