Multiple choice

A right triangle with its sides $9\space cm, 12\space cm$ and $15\space cm$ is revolved about the side $12\space cm$. Find the volume of the solid so formed.

  1. $1018.28\space cm^3$
  2. $702.57\space cm^3$
  3. $652.57\space cm^3$
  4. $752.57\space cm^3$
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A Correct answer
Explanation

Revolving a right triangle around one of its legs creates a cone. The leg it revolves around is the height (h=12), and the other leg is the radius (r=9). Volume = (1/3) * pi * r^2 * h = (1/3) * 3.14159 * 81 * 12 = 1017.876. The option 1018.28 is the closest approximation using a slightly different pi value.

AI explanation

Revolving the right triangle about the 12 cm side forms a cone with a height of 12 cm and a radius of 9 cm. Using the cone volume formula V = 1/3 * pi * r^2 * h, we get 1/3 * 22/7 * 9 * 9 * 12. This simplifies to 1/3 * 22/7 * 972, resulting in a volume of approximately 1018.28 cm^3.

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