Multiple choice

A rectangular paper $11$ cm by $8$ cm can be exactly wrapped to cover the curved surface of a cylinder of height $8$ cm. The volume of the cylinder is

  1. $66$ $\displaystyle cm^{3}$
  2. $77$ $\displaystyle cm^{3}$
  3. $88$ $\displaystyle cm^{3}$
  4. $121$ $\displaystyle cm^{3}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The paper wraps the cylinder, so the circumference = 11 cm and height = 8 cm. 2 * pi * r = 11, so r = 11 / (2 * pi). Volume = pi * r^2 * h = pi * (121 / 4 * pi^2) * 8 = 242 / pi = 77.03. 77 is the correct integer.

AI explanation

When the paper wraps the cylinder, its area equals the curved surface area of the cylinder. The length of the paper wraps around the base, so the circumference is $11$ cm. Using the circumference formula $2\pi r = 11$, we find the radius $r = 11 / (2 \times 22/7) = 7/4$ cm. The volume of the cylinder is $\pi r^2h = (22/7) \times (7/4)^2 \times 8 = 77$ cm$^3$. The volume is 77 cm$^3$.

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