Question

a company uses paper cups shaped like cones for its water cooler. each cup has a height of 15 cm, and the base has a diameter of 10 cm. the cooler has 18,840 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 radius of cone

The diameter $d = 10$ cm, so radius $r=\frac{d}{2}=\frac{10}{2}=5$ cm.

Step2: Find volume of one cone

The volume formula for a cone is $V=\frac{1}{3}\pi r^{2}h$. Substituting $r = 5$ cm, $h = 15$ cm and $\pi=3.14$, we get $V=\frac{1}{3}\times3.14\times5^{2}\times15$.
$V=\frac{1}{3}\times3.14\times25\times15=392.5$ $cm^{3}$.

Step3: Determine number of cups

Let the number of cups be $n$. We know the total volume of water in cooler is $18840$ $cm^{3}$. So $n=\frac{18840}{V}$. Substituting $V = 392.5$ $cm^{3}$, we have $n=\frac{18840}{392.5}=48$.

Answer:

48