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Question

# Two solid metallic right circular cones have same height h. The radii of their bases are r1 and r2. The two cones are melted together and recast into a right circular cylinder of height h. Show that radius of the base of the cylinder is √13(r21+r22).

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True
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False
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Solution

## The correct option is A TrueVolume of the cylinder = Volume of Cone 1 + Volume of Cone 2. Since height is the same for the two cones, let r1 and h be the radius and height of the first cone and r2 and h be the radius and height of the second cone.Volume of a cone =13πr2h, where r is the radius of the base of the cone and h is the height.Volume of a Cylinder of Radius "R" and height "h" =πR2hSo, πR2h=13πr12h+13πr22h⇒R2=13(r12+r22)⇒R=√13(r21+r22)Hence, the radius of the base of the cylinder =√13(r21+r22)

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