Question

a company uses paper cups shaped like cones for its water cooler. each cup has a height of 8 cm, and the base has a diameter of 6 cm. how much water is needed to fill 225 cups? use 3.14 for π, and do not round your answer.

Explanation:

Step1: Find the radius of the cone base

The diameter $d = 6$ cm, so the radius $r=\frac{d}{2}=\frac{6}{2}=3$ cm.

Step2: Calculate the volume of one cone

The volume formula of a cone is $V=\frac{1}{3}\pi r^{2}h$. Substitute $r = 3$ cm, $h = 8$ cm and $\pi=3.14$ into the formula. So $V=\frac{1}{3}\times3.14\times3^{2}\times8=\frac{1}{3}\times3.14\times9\times8 = 3.14\times3\times8=75.36$ $cm^{3}$.

Step3: Calculate the volume of 225 cups

Multiply the volume of one - cup by 225. So the total volume $V_{total}=75.36\times225 = 16956$ $cm^{3}$.

Answer:

$16956$ $cm^{3}$