Brainlet here....

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I was thinking this graphic is misleading because it shows the height of the explosion and explosions are about volume.

I wanted to know how the diameter of a Tsar Bomba blast would compare with the Hiroshima blast.

So.. a sphere is (4pi/3) * r^3. Let's suppose the volume/power of the Hiroshima blast is 1. then 1 Hiroshima Blast Volume = (4pi/3) * r^3. Solving for r we get ((3/(4pi)) ^ (1/3) = r = 0.62035049089 (units of length I hope?)

Tsar Bomba at 5000kt was 333.3 times as powerful as the 15kt Hiroshima blast.

5000 Hiroshima Blast Volumes = (4pi/3) * r^3
So r = ((3 * (5000/15)/(4pi))^(1/3) = 4.30112668869 ( are these Hiroshima blast radii? What units? )

((4 * pi) / 3 ) * (4.30112668869)^(1/3) = 6.81212624003 ( of what?) I thought Tsar Bomba was supposed to be 333.3 times Hiroshima..

What about if we assumed explosions were cubes? Then the formula for volume is l^3.

1 Hiroshima blast volume = 1 Hiroshima blast length ^ 3

1 Hiroshima blast volume ^ (1/3) = 1 Hiroshima Blast Length.

1 Tsar Bomba Blast Volume = 1 Tsar Bomba Blast length ^ 3

5000 Hiroshima Blast Volumes = 1 Tsar Bomba Blast Length ^ 3

((5000/15) Hiroshima Blast Volumes) ^ (1/3) = 1 Tsar Bomba Blast Length = 6.93 (units = Hiroshima blast lengths?)

I feel like I am fumbling around like an idiot.
(1000/15) Hiroshima Blast Volumes ^ (1/3) = 1 Mike Blast Length = 4.05 ( units = hiroshima blast lengths?)