Question

a company makes cones out of solid foam. each cone has a height of 15 inches, and its base has a radius of 1.5 inches. how much foam is needed to make 160 cones? use 3.14 for π, and do not round your answer. in³

Explanation:

Step1: Calculate the volume of one cone

The formula for the volume of a cone is \(V=\frac{1}{3}\pi r^{2}h\). Given \(r = 1.5\) inches, \(h=15\) inches, and \(\pi = 3.14\).
Substitute the values into the formula:
\(V=\frac{1}{3}\times3.14\times(1.5)^{2}\times15\)
First, calculate \((1.5)^{2}=2.25\).
Then \(V=\frac{1}{3}\times3.14\times2.25\times15\)
\(\frac{1}{3}\times15 = 5\)
So \(V=3.14\times2.25\times5\)
\(3.14\times2.25=7.065\)
\(V = 7.065\times5=35.325\) \(in^{3}\)

Step2: Calculate the volume of 160 cones

Multiply the volume of one cone by 160.
\(35.325\times160=(35 + 0.325)\times160\)
\(35\times160+0.325\times160\)
\(35\times160 = 5600\), \(0.325\times160=52\)
\(35.325\times160=5600 + 52=5652\) \(in^{3}\)

Answer:

\(5652\)