Given the rules, we have
[tex]h \approx \dfrac{m}{r^2}[/tex]
Now, let [tex]m, r[/tex] the be mass and radius, respectively, of cylinder X. We know that cylinder Y has mass and radius, respectively, [tex]\frac{m}{4},\ 0.4r[/tex]. So, we have
[tex]h_Y=\dfrac{\frac{m}{4}}{(0.4r)^2} = 1.5625\dfrac{m}{r^2}=1.5625h_X[/tex]
Which implies
[tex]h_Y=1.5625\cdot 12=18.75[/tex]
If the height of cylinder X is 12cm. Then the height of cylinder Y will be 300 cm.
It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
The height h of a cylinder X of a given material varies directly as the mass m and inversely as the square of its radius r.
h ∝ m / r²
If the height of cylinder X is 12cm.
hₓ = 12 cm
It is required to make another cylinder Y of the same material.
If the mass of Y is 1/4times the mass of X and its radius 0.4 times X.
Then the height of the cylinder Y will be
h = (m / 4) / (0.4r)²
Simplify the equation, then the value of the h will be
h = 25 × m / r²
h = 25 × hₓ
h = 25 × 12
h = 300 cm
The height of cylinder Y will be 300 cm.
More about the geometry link is given below.
https://brainly.com/question/7558603
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