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Geometry and Trigonometry / Area and volume Difficulty: Medium

$The figure presents a cylindrical shape with a circular base and a larger circular top. The diameter of the circular base is labeled “k over 2,” the diameter of the circular top is labeled “k,” and the height is labeled “k.” The volume of the figure is equal to the fraction with numerator 7 pi k cubed, and denominator 48$

The glass pictured above can hold a maximum volume of 473 cubic centimeters, which is approximately 16 fluid ounces. What is the value of k, in centimeters?

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Explanation

Choice D is correct. Using the volume formula $V equals, the fraction with numerator 7 pi times k cubed, and denominator 48$ and the given information that the volume of the glass is 473 cubic centimeters, the value of k can be found as follows:

$473 equals, the fraction with numerator 7 pi times k cubed, and denominator 48$

$k cubed equals, the fraction with numerator 473 times 48, and denominator 7 pi, end fraction$

$k equals, the cube root of the fraction with numerator 473 times 48, and denominator 7 pi, end fraction, end root, which is approximately equal to 10 point 1 0 6 9 0$

Therefore, the value of k is approximately 10.11 centimeters.

Choices A, B, and C are incorrect. Substituting the values of k from these choices in the formula results in volumes of approximately 7 cubic centimeters, 207 cubic centimeters, and 217 cubic centimeters, respectively, all of which contradict the given information that the volume of the glass is 473 cubic centimeters.