On a spherical! balloon of radius 10 cm, two dots are put at a distance of 25 units. If the balloon is uniformly expanded to a sphere of radius 50 cm, the distance between the two dots in the same units would be
Given:
Initial radius = 10 cm
Final radius = 50 cm
Initial distance between two dots = 25 units
Let the new distance between the two dots be x units.
Solution:
The key to solving this problem is understanding uniform scaling on a sphere.
If the balloon expands uniformly, then all distances on the surface (arc lengths, distances between points) scale proportionally with the radius.
Final Answer: (b) 125
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