Multiple choice

If the radius of the base of a right circular cone is $3r$ and its height is equal to the radius of the base, then its volume is:

  1. $\cfrac{1}{3}\pi {r}^{3}$
  2. $\cfrac{2}{3}\pi {r}^{3}$
  3. $3\pi{r}^{3}$
  4. $9\pi {r}^{3}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The volume of a cone is (1/3) * pi * r^2 * h. Given the radius is 3r and the height is equal to the radius (3r), the volume is (1/3) * pi * (3r)^2 * (3r) = (1/3) * pi * 9r^2 * 3r = 9 * pi * r^3.

AI explanation

The volume of a right circular cone is calculated as one third times pi times r squared times h. For this cone, the radius is 3r and the height equals the radius, meaning h is also 3r. Substituting these values gives one third times pi times (3r) squared times 3r, which simplifies to 9 times pi times r cubed. The result is 9 times pi times r cubed.

Keep practicing — related questions