Multiple choice

A sphere has the same curved surface as the total surface area of cylinder of height $4$ cm and diameter of base $8$ cm. The radius of the sphere is

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

Cylinder height h=4, diameter d=8 so radius r=4. Total surface area = 2*pi*r*(r+h) = 2*pi*4*(4+4) = 64*pi. Sphere surface area = 4*pi*R^2. Setting 4*pi*R^2 = 64*pi gives R^2 = 16, so R = 4.

AI explanation

Using the total surface area of a cylinder formula 2 * pi * r * (r + h) with radius 4 cm and height 4 cm gives 2 * pi * 4 * (4 + 4) = 64 * pi square cm. Setting this equal to the surface area of a sphere, 4 * pi * R^2, gives 4 * pi * R^2 = 64 * pi. Solving for the sphere radius R yields R = 4 cm.

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