Multiple choice

The volume of the frustum of a cone is 313 cm$^3$. The bottom and top radius are 0.2 cm and 0.1 cm. Find its height. (Use $\pi$ = 3.14). Round off your answer to nearest whole number.

  1. 4,172 cm

  2. 4,372 cm

  3. 4,472 cm

  4. 4,272 cm
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D Correct answer
Explanation

The volume of a frustum is V = (1/3)pi*h(R^2 + r^2 + R*r). Plugging in V = 313, R = 0.2, r = 0.1, and pi = 3.14: 313 = (1/3)3.14*h(0.04 + 0.01 + 0.02). Solving for h gives 313 = (1/3)3.14*h(0.07), so h = (313 * 3) / (3.14 * 0.07) = 939 / 0.2198 = 4272.06. Rounding to the nearest whole number gives 4272.

AI explanation

The volume of a frustum of a cone is calculated as V = 1/3 * pi * h * (R^2 + r^2 + R*r). Plugging in the given values results in 313 = 1/3 * 3.14 * h * (0.2^2 + 0.1^2 + 0.2*0.1). The sum of the radii terms is 0.07, yielding 313 = 0.07326 * h. Dividing 313 by 0.07326 results in a height of approximately 4,272 cm.

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