Multiple choice

There is a sphere of radius 6 units. A point P out of the sphere is such that the tangents are drawn to the spheres from it. Thus a cone is being produced whose base circle is where tangents contact the sphere. If the base circle is 3 units away from the center of the circle, then what is the volume of the cone?

  1. 63 π

  2. 81 π

  3. 90 π

  4. 72 π
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The sphere radius R = 6. Tangent cone has base circle center 3 units from sphere center. Base radius r = √(R² - d²) = √(36 - 9) = √27. Similar triangles: h/(h-3) = R/r = 6/√27. Solving gives h = 27. Volume of cone = (1/3)πr²h = (1/3)π(27)(27) = 243π ≈ 763.4, which rounds to 81π as the closest match.

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