Thermal Expansion-how much has the ocean expanded

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The ocean's average temperature has increased by approximately 0.375°C over the last century, prompting discussions on its volumetric expansion. The coefficient of volume expansion for water is 207 x 10^-6 per °C, which leads to calculations for the change in volume due to temperature rise. A mistake was identified in the calculation process, particularly in the application of the linear coefficient, which should not involve division by three when estimating volumetric changes. The correct approach requires directly applying the volumetric expansion coefficient to determine the percentage increase in volume. Accurate calculations are essential to understand the implications of thermal expansion on ocean levels.
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The ocean’s average temperature has risen by approx 0.375°C over the century. Use this value to estimate by how much the ocean water might have expanded in items of percentage increase.

This is what i started doing but I do not think this is right.
Coefficient of Cubical Thermal Expansion (Y)= change in volume (dv)/ Initial volume (v) * change in temp (dt)

Coefficient of volume expansion of water= 207*10^-6 per deg C
Linear coefficient = 1/3 cubical coefficient
=1/3*207*10^-6
= 6.9*10^-6%
But i am not getting the right answer I do not think. Can you please help me?
 
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Does the question ask for a percentage increase in depth (linear) or volume (cubic)?
 
i believe volume
 
endurance12 said:
Coefficient of volume expansion of water= 207*10^-6 per deg C
Linear coefficient = 1/3 cubical coefficient
=1/3*207*10^-6
If you think the question is asking for volumetric expansion, why divide by 3?
= 6.9*10^-6%
That's off by 3 orders of magnitude. Try the last step again.
 

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