Mathematics

Two right circular cones x and y are made. x having three times the radius of y and y having half the volume of x. Calculate the ratio between the heights of x and y.

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For y cone,

⇒ Radius (r) = a cm,

⇒ Height = h cm,

⇒ Volume = V cm³.

∴ $\dfrac{1}{3}πr^2h = V$

⇒ $\dfrac{1}{3}πa^2h = V$ …………(1)

For x cone,

⇒ Radius (r₁) = 3a cm,

⇒ Height = h₁ cm,

⇒ Volume = 2V cm³.

∴ $\dfrac{1}{3}πr$

⇒ $\dfrac{1}{3}π(3a)^2h_1 = 2V$ …………(2)

Dividing equation (2) by (1), we get :

$\Rightarrow \dfrac{\dfrac{1}{3}π9a^2h$

h₁ : h = 2 : 9.

Hence, the ratio between heights of x and y = 2 : 9.

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