Explanation:
V = pi×h/3 (R² + Rr + r²) where "V", "h", "R" and "r" are volume, height, larger "rim" radius, and smaller base radius of the conical cylinder (here beaker and tank).
since the beaker and the tank are similar, this means that there is one constant scaling factor for all the corresponding lines between the 2 shapes.
that means that
height of beaker × f = height of tank
has the same "f" as
base radius of beaker × f = base radius of tank.
the same for R ("rim" radius).
and so on.
that means that in the volume formula for the tank the factor "f" is brought in as f³ (product of "f" in "h" and of "f²" in every radius term of the summary terms in the brackets).
so,
Vtank = Vbeaker × f³
therefore,
1728 = f³
f = 12
and the base radius of the tank is
8 × 12 = 96 cm
the height of the tank is
15 × 12 = 180 cm