Multiple choice

Find the volume of a right circular cylinder of height $10$ inscribed in a sphere of radius $6$. (in standard units)

  1. $104$
  2. $346$
  3. $545$
  4. $785$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Cylinder height h=10, radius r. Sphere radius R=6. Cylinder radius r^2 + (h/2)^2 = R^2. r^2 + 25 = 36, so r^2 = 11. Volume = pi * r^2 * h = pi * 11 * 10 = 110 * 3.14159 = 345.57. Rounded to 346.

AI explanation

For a cylinder of height 10 inscribed in a sphere of radius 6, half of the cylinder's height and the sphere's radius form the hypotenuse of a right triangle with the cylinder's radius. Using the Pythagorean theorem, the cylinder's radius r satisfies r^2 + 5^2 = 6^2, so r^2 = 11. The volume of a cylinder is V = pi*r^2*h, which gives V = pi*(11)*(10) = 110*pi, or approximately 346.

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