Multiple choice

From a solid right circular cylinder with height $h$ and radius of the base $r$, a right circular cone of the same height and same base is removed. Find the volume of the remaining solid.

  1. $\displaystyle \frac{2}{3}\, \pi r^{2}h$
  2. $ \pi r^{2}h$
  3. $2 \pi r^{2}h$
  4. $\displaystyle \frac{1}{3}\, \pi r^{2}h$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume of cylinder = pi * r^2 * h. Volume of cone = (1/3) * pi * r^2 * h. Remaining volume = pi * r^2 * h - (1/3) * pi * r^2 * h = (2/3) * pi * r^2 * h.

AI explanation

The volume of the remaining solid is found by subtracting the volume of the right circular cone from the volume of the right circular cylinder. Using the formulas for their volumes, the cylinder has a volume of pi times r squared times h and the cone has a volume of one third times pi times r squared times h. Subtracting the cone from the cylinder gives two thirds times pi times r squared times h.

Keep practicing — related questions