Multiple choice

The base and top radius of a cone is 36 cm and 16 cm respectively. The height of the cone is 12.6 cm. What is the volume of frustum of a cone? (Use $\pi$ = 3.14).

  1. 28,064.064 cm$^3$
  2. 27,064.064 cm$^3$
  3. 26,064.064 cm$^3$
  4. 25,064.064 cm$^3$
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A Correct answer
Explanation

Volume of frustum = (1/3) * pi * h * (R^2 + r^2 + R*r). R=36, r=16, h=12.6. V = (1/3) * 3.14 * 12.6 * (36^2 + 16^2 + 36*16) = 1.0466 * 3.14 * (1296 + 256 + 576) = 13.188 * 2128 = 28064.064.

AI explanation

Using the frustum volume formula V = (1/3) * pi * h * (R^2 + r^2 + R*r), substitute R = 36, r = 16, h = 12.6, and pi = 3.14. Calculate the radii components as 36^2 = 1296, 16^2 = 256, and 36 * 16 = 576, which sum to 2128. Multiply the values to get (1/3) * 3.14 * 12.6 * 2128 = 13.188 * 2128 = 28,064.064 cm^3.

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