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

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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

`V_s={4pi12^3}/3`

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

`V_l={4pi(12+1.09361)^3}/3={4pi13.09361^3}/3`

The volume increase is:

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

`=13.09361^3/12^3`

`=2244.8/1728`

`=1.2991`

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

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