Multiple choice

The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are $12$ cm each. The radius of the sphere is:

  1. $3$ cm
  2. $4$ cm
  3. $6$ cm
  4. $12$ cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Surface area of sphere = 4 * pi * r^2. Cylinder: h = 12, d = 12, so radius r_c = 6. Curved surface area = 2 * pi * r_c * h = 2 * pi * 6 * 12 = 144 * pi. 4 * pi * r^2 = 144 * pi => r^2 = 36 => r = 6.

AI explanation

The surface area of the sphere is equated to the curved surface area of the right circular cylinder. The cylinder has a height of 12 cm and a diameter of 12 cm, giving a radius of 6 cm. Using the curved surface area formula 2 * pi * R * H, the cylinder's area is 2 * pi * 6 * 12 = 144 pi square cm. Setting the sphere's surface area formula 4 * pi * r^2 equal to 144 pi gives r^2 = 36, so the radius of the sphere is 6 cm.

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