What is the ratio of the base-radius and slant height of a cone made by rolling up a semicircle?

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Solution

Let the radius of the bigger circle be R units.

∴ Slant height of the cone = Radius of the bigger circle = R units

Since the cone is made from a semi-circular sector, the central angle = = 180°.

∴ Radius of the small circle = of the radius of the larger circle

∴ Base-radius of the cone

Therefore, ratio of the base radius to the slant height of the cone is 1:2.

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