Multiple choice

The trunk of a tree is a right cylinder $1.5 m$ in radius and $10 m$ high. What is the volume of the timber which remains when the trunk is trimmed just enough to reduce it to a rectangular parallelogram on a square base?

  1. $45m^{2}$
  2. $54 m^2$
  3. $50 m^2$
  4. $48 m^2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The square base that fits inside a circular cross-section has diagonal 3 m, so its side is 3/sqrt(2) m. The remaining timber is a square prism with volume 45 cubic m, not 45 square m, so the numerical value matches but the stated unit is wrong.

AI explanation

The square base inscribed in the circular cross-section has a diagonal equal to the diameter of the cylinder, which is 2 multiplied by 1.5 to equal 3 m. Using the Pythagorean theorem, the side of the square is 3 divided by the square root of 2. The volume of the resulting rectangular parallelepiped is the area of this square base multiplied by the height: (9/2) multiplied by 10 equals 45 cubic meters. The volume of the timber is 45.

Keep practicing — related questions