The notation
... Figure A ~ Figure B
means the two figures have the same proportions. (They are similar.) Every dimension of the larger figure is 5/2 times the corresponding dimension of the smaller figure. (You know this is the ratio because you are given the radius measures.)
The constant of proportionality of volume is the cube of the constant of proportionality of the linear measures (such as radius or height). So, the larger volume is
... (5/2)³×(88 ft³) = 1375 ft³
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The formula for volume is
... V₁ = πr²h
When r and h are larger by a factor of 5/2, this is
... V₂ = π(5/2·r)²·(5/2·h) = πr²h·(5/2)³
... V₂ = V₁·(5/2)³ . . . . as discussed above