Question
Download Solution PDFIf the radius of a sphere is doubled, then the volume of the sphere becomes _____ times the previous volume.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
If the radius of a sphere is doubled, then the volume of the sphere becomes _____ times the previous volume.
Concept:
The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius.
Formula Used:
Volume of Sphere: V = (4/3)πr³
Calculation:
Let the initial radius be r.
Initial volume, Vinitial = (4/3)πr³
When the radius is doubled, the new radius = 2r.
New volume, Vnew = (4/3)π(2r)³
⇒ Vnew = (4/3)π(8r³)
⇒ Vnew = 8 × (4/3)πr³
⇒ Vnew = 8 × Vinitial
∴ The volume of the sphere becomes 8 times the previous volume when the radius is doubled.
Last updated on May 28, 2025
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