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A spherical balloon is inflated until its radius is 20% greater than before. By what percentage does its outer surface increase?

Competition practiceMensuration
  • A20%
  • B44%
  • C40%
  • D72.8%

Step-by-Step Solution

A sphere's surface is 4π, so it scales as the SQUARE of the radius: the new surface is times the old, an increase of 44%. The trap 20% applies the linear growth straight to the surface; 40% doubles the 20% and drops the small 0.04 term that squaring produces; 72.8% is the increase in the balloon's VOLUME, since , a cubic answer offered where a surface was asked.
Answer: B) 44%

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