Question
The ratio of the radii of two spheres is 2 : 3. If the radius of the first sphere is increased by 50% and the radius of the second sphere is increased by 20%, find the ratio of their new volumes.
This question was previously asked in
RRB NTPC 2025 Under Graduate CBT 1 Question Paper PDF (20-Jun-2026) (Shift 3)
The correct answer is
125 : 216
Let the radii be 2r and 3r. New radii: \(2r\times1.5=3r\) and \(3r\times1.2=3.6r\).
Volume ratio: \((3r)^3 : (3.6r)^3 = 27 : 46.656\).
Since \(3.6 = \tfrac{18}{5}\), \((3.6)^3 = \tfrac{5832}{125}\), so the ratio becomes \(27 : \tfrac{5832}{125} = 3375 : 5832 = 125 : 216\).
Hence, the ratio of their new volumes is 125 : 216.
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