Multiple choice

If the height of the cone is half the radius of the sphere, then the radius of the base of a cone which has the same volume as a sphere of $5$ cm radius, is

  1. $10$ cm
  2. $\displaystyle 10\sqrt{2}$ cm
  3. $\displaystyle \frac{5\sqrt{2}}{2}$ cm
  4. $\displaystyle \frac{10\sqrt{3}}{3}$ cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume of sphere = 4/3 * pi * 5^3 = 500/3 * pi. Volume of cone = 1/3 * pi * r^2 * h. Given h = 5/2. So 500/3 * pi = 1/3 * pi * r^2 * 5/2. 500 = r^2 * 5/2. r^2 = 200. r = sqrt(200) = 10*sqrt(2).

AI explanation

The sphere has a radius of 5 cm, so its volume is four thirds times pi times 5 cubed, which is 500 pi divided by 3. The cone has height h equal to half of 5 cm, so h equals 2.5 cm, and setting its volume one third times pi times radius squared times h equal to the sphere volume gives one third times pi times radius squared times 2.5 equals 500 pi divided by 3. Solving this equation gives radius squared equals 200, so the radius is 10 times the square root of 2 cm.

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