Multiple choice

In Figure, the radius of the base of the right circular cone is $3$. If the volume of the cone is $12\pi$, find the lateral area of the cone.

  1. $12\pi$
  2. $15\pi$
  3. $18\pi$
  4. $36\pi$
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B Correct answer
AI explanation

The volume of a cone equals one third times pi times the square of the radius times the height, which gives the equation 12 pi equals one third times pi times 3 squared times the height. Solving this shows the height is 4. Using the Pythagorean theorem, the slant height is the square root of the sum of 3 squared and 4 squared, which is 5. The lateral area is pi times the radius times the slant height, giving an area of 15 pi.

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