Multiple choice

A right circular cone and a sphere have equal volumes. If the radius of the base of the cone is $2x$ and the radius of the sphere is $3x$, find the height of the cone in terms of $x$.

  1. $x$
  2. $\dfrac{3x}{2}$
  3. $\dfrac{4x}{3}$
  4. $20x$
  5. $27x$
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Volume of cone = (1/3) * pi * (2x)^2 * h = (4/3) * pi * x^2 * h. Volume of sphere = (4/3) * pi * (3x)^3 = (4/3) * pi * 27x^3. Equating: (4/3) * pi * x^2 * h = (4/3) * pi * 27x^3. h = 27x.

AI explanation

The volume of a right circular cone is (1/3)πr^2h and the volume of a sphere is (4/3)πR^3. Equating the volumes gives (1/3)π(2x)^2h = (4/3)π(3x)^3. Simplifying this yields (4/3)x^2h = 36x^3, so h = 27x. The result is 27x.

Keep practicing — related questions