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The corresponding heights are linear measures (1st-degree), while the volumes are 3rd-degree. I am going to reach a little here, and suppose that you meant for cylinder B to have volume 3600 cm³, not cm², which would make no sense. Let h cm be the unknown height of cylinder B

h³ : 10³ = 3600 : 450

h³ : 1000 = 8 : 1

h³ = 8000

h = 20

The height is 20 cm.

Using the ratios

linear = a : b

Area = a^2 : b^2

Volume = a^3 : b^3

Hence the volume rat'os of A : B is 450 : 3600 = 45 :360 = 5 : 40

Hence a^3 : b^3 = 5 : 40

Cube root

a : b = 5^(1/3) : 40^(1/3) = 1.7099 : 3.1499

Hence

10/ 1.7099 = b/3.1499

b = 10 X 3.14999 / 1.7099 = 20.0000 = 20 cm .

A and B are two similar cylinders.

 The height of cylinder A is 10 cm and its volume is 450 cm^3 .

The volume of cylinder B is 3600 cm^3.

  The height of cylinder B is 20 cm.

Let hA and rA be the height and radius of cylinder A and hB and rB be the height and radius of cylinder B. Because they're similar,

h1/h2 = r1/r2

450 = 10pi r1^2

r1^2 = 45/pi

r1 = √(45/pi)

3600 = h2pi r2^2

r2^2 = 3600/(h2pi)

r2 = 60/√(h2 pi)

Substitute for r1 and r2 in h1/h2 = r1/r2:

10/h2 = √(45/pi)/(60/√(h2 pi))

10/h2 = √(45/pi) * √(h2 pi)/60

10/h2 = √45√h2)/60

600/h2 = √45√h2

600/√45 = h2^(3/2)

h2 = (600/√45)^(2/3) = 20 cm