Question

a company makes cones out of solid foam. each cone has a height of 18 inches, and its base has a radius of 3 inches. how much foam is needed to make 25 cones? use 3.14 for π, and do not round your answer.
□ in³

Explanation:

Step1: Recall the volume formula for a cone

The volume \( V \) of a cone is given by the formula \( V=\frac{1}{3}\pi r^{2}h \), where \( r \) is the radius of the base and \( h \) is the height of the cone.

Step2: Substitute the given values into the formula for one cone

We are given that \( r = 3 \) inches and \( h=18 \) inches, and \( \pi=3.14 \). Substituting these values into the formula:
\( V=\frac{1}{3}\times3.14\times3^{2}\times18 \)
First, calculate \( 3^{2}=9 \). Then the expression becomes \( \frac{1}{3}\times3.14\times9\times18 \).
\( \frac{1}{3}\times9 = 3 \), so now we have \( 3.14\times3\times18 \).
\( 3\times18 = 54 \), so \( V = 3.14\times54=169.56 \) cubic inches for one cone.

Step3: Calculate the volume for 25 cones

To find the volume of foam needed for 25 cones, we multiply the volume of one cone by 25.
\( \text{Total Volume}=25\times169.56 \)
\( 25\times169.56 = 4239 \)

Answer:

4239