Question

a company makes cones out of solid foam. each cone has a height of 9 inches, and its base has a radius of 2.5 inches. how much foam is needed to make 120 cones? use 3.14 for π, and do not round your answer. in³

Explanation:

Step1: Calculate the volume of one cone

The volume formula of a cone is \(V=\frac{1}{3}\pi r^{2}h\). Given \(r = 2.5\) inches, \(h=9\) inches, and \(\pi = 3.14\).
Substitute the values into the formula:
\(V=\frac{1}{3}\times3.14\times(2.5)^{2}\times9\)
First, calculate \((2.5)^{2}=6.25\).
Then, \(\frac{1}{3}\times9 = 3\).
So \(V=3\times3.14\times6.25\)
\(V = 9.42\times6.25=59.25\) \(in^{3}\)

Step2: Calculate the volume of 120 cones

Multiply the volume of one cone by 120.
\(V_{total}=59.25\times120\)
\(V_{total}=7110\) \(in^{3}\)

Answer:

\(7110\)