Multiple choice

A cup is in the form of a hemisphere surmounted by a cylinder. The height of the cylindrical portion is 9 cm and the total height of the cup is 12.5 cm. Then the radius of the cylindrical portion is

  1. 3.5 cm

  2. 2.5cm

  3. 21.5cm

  4. 9 cm

  5. None of these
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A Correct answer
Explanation

The total height of the cup is the sum of the cylinder height and the hemisphere radius. Since the total height is 12.5 cm and the cylinder height is 9 cm, the radius is 12.5 - 9 = 3.5 cm.

AI explanation

The total height of the cup includes the height of the cylindrical portion plus the radius of the hemispherical portion, since they share the same base radius. Using the equation Total height = Cylinder height + Sphere radius, we get 12.5 = 9 + r. Solving for r gives r = 3.5 cm. The radius of the cylindrical portion is 3.5 cm.

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