Multiple choice

A sphere of radius $4$ cm has the same volume as that of a cone with a circular base of radius $4$ cm.The height of the cone is

  1. $12$ cm
  2. $16$ cm
  3. $20$ cm
  4. $24$ cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume of sphere = (4/3) * pi * 4^3 = 256pi/3. Volume of cone = (1/3) * pi * 4^2 * h = 16pi*h/3. Equating: 256/3 = 16h/3, so h = 16.

AI explanation

Using the volume formulas for a sphere and a cone, we set (4/3)pi*R^3 equal to (1/3)*pi*r^2*h. Given the sphere's radius is 4 cm and the cone's base radius is 4 cm, the equation becomes (4/3)*pi(4)^3 = (1/3)pi(4)^2*h. Canceling the common terms leaves 4 * 4 = h, which means the height of the cone is 16 cm.

Keep practicing — related questions