Multiple choice

A hemispherical dome rests on its circular base. A cylinder is placed inside the dome with one of its bases resting on the base of the dome. Find the radius of the largest possible cylinder that can be placed, if the radius of the hemisphere is 10√(3/2)

  1. 8

  2. 10

  3. 9

  4. 11
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For a cylinder of radius r and height h inside a hemisphere of radius R, the relationship is r^2 + h^2 = R^2. To maximize volume V = pi * r^2 * h, we find that the optimal radius is R * sqrt(2/3). Given R = 10 * sqrt(3/2), r = 10 * sqrt(3/2) * sqrt(2/3) = 10.

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