Multiple choice

A vessel is in the form of a frustum of a cone. Its radius at top end is 12 m and the bottom end is 10 m. Its volume is 369 $ \pi m^3$. Find its height.

  1. 3.64 m

  2. 3.04 m

  3. 3.54 m

  4. 3.44 m
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B Correct answer
Explanation

The volume of a frustum is V = (1/3) * pi * h * (R^2 + r^2 + R*r). Plugging in V = 369 * pi, R = 12, r = 10: 369 = (1/3) * h * (144 + 100 + 120). 369 = (1/3) * h * 364. h = (369 * 3) / 364 = 3.041 m.

AI explanation

The volume of a frustum of a cone is found using the formula V equals one third times pi times height times the sum of the squares of the two radii plus their product. Setting up the equation, 369 times pi equals one third times pi times height times (12 squared plus 10 squared plus 12 times 10). This simplifies to 1107 equals height times (144 plus 100 plus 120), so 1107 equals 364 times height. Dividing 1107 by 364 gives a height of approximately 3.04 m.

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