Question

a company uses paper cups shaped like cones for its water cooler. each cup has a height of 6 cm, and the base has a radius of 3.5 cm. how much water is needed to fill 200 cups? use 3.14 for π, and do not round your answer.

Explanation:

Step1: Calculate the volume of one conical cup

The formula for the volume of a cone is \(V=\frac{1}{3}\pi r^{2}h\). Given \(r = 3\space cm\), \(h=6\space cm\) and \(\pi = 3.14\).
Substitute the values into the formula: \(V=\frac{1}{3}\times3.14\times3^{2}\times6\).
First, calculate \(3^{2}=9\). Then \(\frac{1}{3}\times9 = 3\). So \(V=3\times3.14\times6\).
\(3\times6 = 18\), then \(V=3.14\times18= 56.52\space cm^{3}\).

Step2: Calculate the total volume for 200 cups

Multiply the volume of one cup by 200. So \(V_{total}=56.52\times200 = 11304\space cm^{3}\). Since \(1\space cm^{3}=1\space ml\) (volume of water), the amount of water needed is \(11304\space ml\).

Answer:

\(11304\space ml\)