Multiple choice

The volume of a right cone is 924$\displaystyle m^{2}$ and its height is 18 m then lateral surface area is

  1. $\displaystyle 22\sqrt{115}m^{2}$
  2. $\displaystyle 310m^{2}$
  3. $\displaystyle 22\sqrt{373}m^{2}$
  4. $\displaystyle 276m^{2}$
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C Correct answer
Explanation

Interpreting the stated volume as 924 m^3, use (1/3)pi r^2 x 18 = 924 to obtain r = 7 m. The slant height is sqrt(7^2 + 18^2) = sqrt(373), so the lateral area is pi x 7 x sqrt(373) = 22sqrt(373) m^2.

AI explanation

Using the cone volume formula V = 1/3 times pi times r squared times h, we write 924 equal to 1/3 times 22/7 times r squared times 18. Solving this gives the radius r as 7 m. The slant height l is the square root of (r squared plus h squared), which is the square root of (7 squared plus 18 squared) to equal the square root of 373. The lateral surface area is pi times r times l, resulting in 22/7 multiplied by 7 and the square root of 373, to equal 22 times the square root of 373.

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