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The question asked may be included in your lab course in biology but relates to the Ideal Gas Law in chemistry. This law provides a very close approximation to how gases behave under different temperatures and pressures.
The ideal gas law relates the volume (V) occupied by n moles of a gas under a pressure P and at a temperature T.
P*V = n*R*T where R is a constant approximately equal to 8.314 J/K*mole
Rearranging the terms of the equation: V = n*R*T/P
In a balloon the gas is under a constant pressure exerted by the atmosphere, the amount of substance that makes up the gas also remains the same. This makes the volume proportional to the temperature or V = K*T
It is being assumed that the balloon is spherical in shape. The volume of a sphere with diameter d is (4/3)*pi*(d/2)^3.
The graph of the balloon's diameter is a curve where the diameter is directly related to the cube root of the temperature.
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