Question
Download Solution PDFIf the radius of a sphere is tripled, what is the ratio of the volume of the original sphere to that of the new sphere?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The radius of the original sphere = r
The radius of the new sphere = 3r
Formula Used:
Volume of a sphere = \(\frac{4}{3}\pi r^3\)
Calculation:
Volume of the original sphere = \(\frac{4}{3}\pi r^3\)
Volume of the new sphere = \(\frac{4}{3}\pi (3r)^3\)
⇒ Volume of the new sphere = \(\frac{4}{3}\pi (27r^3)\)
⇒ Volume of the new sphere = \(27 × \frac{4}{3}\pi r^3\)
⇒ Volume of the new sphere = 27 × Volume of the original sphere
Ratio of the volume of the original sphere to the new sphere = 1 : 27
The correct answer is option 2.
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