If the radius of the balloon is increased by 1meter, by what percent is the enclosed volume increased? A hot air balloon in the shape of a sphere hasa radius of 12 yards. 

Expert Answers

An illustration of the letter 'A' in a speech bubbles

One meter is 1.09361 yards.  Also, the volume of a sphere is 

`V={4pir^3}/3` , so the volume of a sphere with radius 12 yards is


and the volume of a sphere with radius 12 yards + 1 meter is


The volume increase is:

`V_l/V_s={4pi13.09361^3}/3 times 3/{4pi12^3}`




This means the balloon has increased by a ratio 0.2991 which is 29.91%.

Approved by eNotes Editorial Team

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial