Answer :

Let the radius of the base of conical ice cream = x cm

Then, height of the conical ice cream = 2 × diameter

= 2 × (2x)

= 4x cm

Volume of ice- cream cone

= Volume of conical portion + Volume of hemispherical portion

= 2πx^{3} cm^{3}

Now,

Diameter of cylindrical container = 12cm

So, radius = 6cm

and height = 15cm

∴ Volume of cylindrical container = πr^{2}h

= π × (6)^{2} × (15)

= 540π cm^{3}

⇒ x^{3} = 27

⇒ x = 3

So, the radius of the base of conical ice cream is 3cm

Hence, the diameter of the base of conical ice-cream = 2×3 = 6cm

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