A 72.8% volume increase gives a factor of 1.728. Since volume scales cubically with radius, the new radius factor is ∛1.728 = 1.2. This represents a 20% increase, so x = 20.
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Class 9 maths ganita manjari part 2 chapter 14 question answer
Let the initial radius be r and initial volume be V = (4/3)πr³. An increase in volume of 72.8% gives new volume V’ = 1.728V. Because volume is proportional to the cube of the radius, (r’)³ = 1.728r³. Taking the cube root gives r’ = 1.2r = r + 0.2r, which corresponds to a 20% increase. Thus, x = 20.
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