What is 'it'. Please clarify!!!!!
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It would depend on what calculation you are solving.
You do not solve the diameter. You can either measure it or you can CALCULATE it. Calculation depends on what information you do have. There are different formulae which depend on whether you know the radius, the circumference, the area, the volume (if a sphere), the angle between tangents from a point at a known distance from the centre etc.
Algebra is needed to solve any complex calculation involving an unknown variable. Everything from computer games to flying to the moon relies upon algebra to calculate variables required.
I would certainly bet on a computer. Try to solve (log z)^-3i. This is log z raised to the -3i power. A computer comes in handy.
You do not need to write anything to calculate things mentally.