Multiple choice

If the volumes of a cone and a hemisphere having the same base are equal, then the height of the cone will be $x$ times the radius of the base of hemisphere, where $x$ is

  1. $1$
  2. $2$
  3. $3$
  4. $\pi$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume of cone = (1/3) * pi * r^2 * h. Volume of hemisphere = (2/3) * pi * r^3. Setting them equal: (1/3) * pi * r^2 * h = (2/3) * pi * r^3. h = 2r. Thus, x = 2.

AI explanation

Equating the volume of the cone, (1/3)*pi*r^2*h, to the volume of the hemisphere, (2/3)*pi*r^3, gives (1/3)*pi*r^2*h = (2/3)*pi*r^3. Canceling the common terms of (1/3)*pi*r^2 from both sides results in h = 2r. Therefore, the height of the cone is 2 times the radius of the base.

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