Need help about reactor (inductor)

[MissP.25_5]

Can someone help me solve this? I don't really understand how to do this.

A 1kvA reactor's capacity is needed to be enlargedto 81kvA. How much does its dimension needs to be multiplied?

Hint:
when its dimension is m times enlargened, surface A'=m'A, flux ∅'=m^2∅, current I'=m^2I, voltage E'=m^2E, Capacity E'I'=m^4EI.

Loss Pe'=m^3Pe
Temperature θ'=loss/surface area = (m^3Pe)/m^2A = mθ

My attempt:
Capacity E'I'=m^4EI. So,
E'I' / EI = m^4
81/1 = m^4
m = 3.

Is the answer 3?

 

[Simon Bridge]

Looks like a straight scaling to me too.
It helps if you lay it out formally:

If capacity is given by ##\small C=EI##
And you know the E and I scale by: ##\small E'=m^{\tiny 2}E## and ##\small I'=m^{\tiny 2}I##; then $$C'=E'I'=m^4EI=m^4C$$
The only way you can get this wrong is if any of these relations are wrong, or if you hit the wrong buttons on your calculator.

Your answer is saying you need to increase the characteristic dimension of the reactor to 3x it's current size to get an 81x increase in capacity.