Multiple choice

Find the radius of a cone . The height of the cone is $10$ ft and its volume is $\displaystyle 440{ ft }^{ 3 }$. (use $\displaystyle \pi =\frac { 22 }{ 7 } $).

  1. $6.2$ ft
  2. $6.0$ ft
  3. $5.2$ ft
  4. $6.4$ ft
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D Correct answer
Explanation

Volume of a cone = (1/3) * pi * r^2 * h. 440 = (1/3) * (22/7) * r^2 * 10. 440 * 3 * 7 / (22 * 10) = r^2. 44 * 21 / 22 = r^2. 2 * 21 = r^2. 42 = r^2. r = sqrt(42) which is approx 6.48.

AI explanation

Using the cone volume formula V = 1/3*pi*r^2*h, substitute the volume 440 and height 10 to get 440 = 1/3 * 22/7 * r^2 * 10. This simplifies to 440 = 220/21 * r^2, so r^2 = 42. Taking the square root gives a radius of approximately 6.4 ft.

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