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. cups

Explanation:

Step1: Find the radius of the cone

The diameter \(d = 12\) cm. The radius \(r=\frac{d}{2}\).
\(r=\frac{12}{2}=6\) cm.

Step2: Calculate the volume of one conical cup

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.
Substitute the values into the formula:
\(V=\frac{1}{3}\times3.14\times6^{2}\times10\).
First, calculate \(6^{2}=36\).
Then \(V=\frac{1}{3}\times3.14\times36\times 10\).
\(\frac{1}{3}\times36 = 12\).
So \(V=3.14\times12\times10\).
\(V = 376.8\) \(cm^{3}\).

Step3: Find the number of cups

Let \(n\) be the number of cups. We know the total volume of water is \(16956\) \(cm^{3}\).
Using the formula \(n=\frac{\text{Total volume}}{\text{Volume of one cup}}\).
\(n=\frac{16956}{376.8}\).
\(n = 45\).

Answer:

\(45\)