Multiple choice

A cloth having an area of $165\ m^2$ is shaped into the form of a conical tent of radius $5\ m$. Find the volume of the cone.

  1. $241.74\ m^2$
  2. $240\ m^2$
  3. $250.48\ m^2$
  4. $260\ m^2$
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A Correct answer
Explanation

For the tent, 165 = π(5)l gives a slant height of about 10.5 m. The vertical height is about 9.23 m, so the volume is (1/3)π(5^2)(9.23) ≈ 241.74 m^3.

AI explanation

The cloth area forms the curved surface of the conical tent, so pi * r * l = 165. With a radius of 5, the slant height l is calculated as 165 divided by 5 pi, resulting in 10.5. Using the Pythagorean theorem, the height is the square root of 10.5 squared minus 5 squared, which is 9. The volume of the cone is calculated as (1/3) * pi * 5^2 * 9, yielding 241.74.

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