Multiple choice

A right circular cylinder has its height equal to two times its radius. It is inscribed in a right circular cone having its diameter equal to 10 cm and height 12 cm, and the axes of both the cylinder and the cone coincide. Then, the volume (in cm3) of the cylinder is approximately

  1. 107.5

  2. 118.6

  3. 127.5

  4. 128.7
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using similar triangles, the radius r and height h of the cylinder satisfy r/h = (5-r)/h_cone_remaining. With h=2r, height of cone=12, radius of cone=5, we get r/(5-r) = 12/5, leading to r = 60/17. Volume = pi * r^2 * h = pi * (60/17)^2 * (120/17) approx 127.5.

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