Question

a company makes cones out of solid foam. each cone has a height of 12 inches, and its base has a diameter of 3 inches. how much foam is needed to make 150 cones? use 3.14 for π, and do not round your answer. in³

Explanation:

Step1: Calculate the radius of the cone's base

The diameter \(d = 3\) inches. The radius \(r=\frac{d}{2}=\frac{3}{2}=1.5\) inches.

Step2: Find the volume of one cone

The formula for the volume of a cone is \(V=\frac{1}{3}\pi r^{2}h\). Substitute \(r = 1.5\), \(h=12\), and \(\pi = 3.14\) into the formula.

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Step3: Calculate the total volume for 150 cones

Multiply the volume of one cone by 150. \(V_{total}=28.26\times150 = 4239\)

Answer:

\(4239\)