Question

a company uses paper cups shaped like cones for its water cooler. each cup has a height of 10 cm, and the base has a diameter of 12 cm. the cooler has 16,956 cm³ of water in it. how many cups can be filled from the cooler? use 3.14 for π, and do not round your answer.

Explanation:

Step1: Calculate the radius of the cup's base

The diameter of the base is \(d = 12\) cm, so the radius \(r=\frac{d}{2}=\frac{12}{2}=6\) cm.

Step2: Calculate the volume of one cup (cone - shaped)

The volume formula for a cone is \(V=\frac{1}{3}\pi r^{2}h\). Given \(h = 10\) cm and \(\pi=3.14\), \(r = 6\) cm.

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Step3: Calculate the number of cups

The total volume of water in the cooler is \(V_{total}=16956\space cm^{3}\). The number of cups \(n=\frac{V_{total}}{V}\).

$$ n=\frac{16956}{376.8}=45 $$

Answer:

45