Multiple choice

The ratio of the total surface area and the lateral surface area of a right cone is 4 : 3 and its height is 8 m, then its base area is approx

  1. $\displaystyle 24m^{2}$
  2. $\displaystyle 33m^{2}$
  3. $\displaystyle 21m^{2}$
  4. $\displaystyle 27m^{2}$
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AI explanation

Let r be the base radius and l be the slant height; the ratio of total surface area to lateral surface area gives pi times r squared plus pi times r times l divided by pi times r times l equals 4/3. This simplifies to r divided by l plus 1 equals 4/3, meaning l equals 3 times r. Using the height of 8 m in the Pythagorean theorem, the square root of (r squared plus 8 squared) equals 3 times r, so r squared plus 64 equals 9 times r squared, yielding r squared equals 8. Using pi as 22/7, the base area pi times r squared is 22/7 multiplied by 8, which is approximately 25.1 m squared, making 24 m squared the closest approximation.

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