Multiple choice

If the radius and height of a cone are in the ratio 5 : 12 and its volume is $314 cm^3$, then its slant height is

  1. 12 cm

  2. 10 cm

  3. 13 cm

  4. 15 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Radius r = 5k, height h = 12k. Volume = (1/3) * pi * r^2 * h = 314. (1/3) * 3.14 * (25k^2) * (12k) = 314. 3.14 * 100k^3 = 314 => k^3 = 1 => k = 1. So r = 5, h = 12. Slant height l = sqrt(r^2 + h^2) = sqrt(25 + 144) = 13.

AI explanation

Let the radius be 5x and the height be 12x according to the given ratio. Using the volume of a cone formula, (1/3) * pi * r^2 * h = 314, we substitute the values to get (1/3) * (314/100) * (25x^2) * (12x) = 314. Solving this equation yields x = 1, meaning the radius is 5 cm and the height is 12 cm. Applying the Pythagorean theorem, the slant height is the square root of (5^2 + 12^2), which equals 13 cm.

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