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A spherical balloon is partially blown up and its surface area is measured More air is then added increasing the volume of the balloon If the surface area of the balloon expands by a factor of 3.7?
IBEE4LIFE
Area varies as (radius)2.
Volume varies as (radius)3 = (area)3/2
If area increased by the factor of 3.7, then volume increased by the factor of (3.7)3/2 = 7.117 times (rounded)
Wiki User
∙ 14y ago
The volume of the balloon will increase by a factor of approximately 3.7^(3/2) or roughly 10.53. Since volume is proportional to the cube of the radius, and surface area is proportional to the square of the radius, when the surface area expands by a factor of 3.7, the volume expands by a factor of (3.7)^(3/2).
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