Question

a company makes wax candles in the shape of a cylinder. each candle has a diameter of 6 inches and a height of 4 inches. how much wax will the company need to make 140 candles? use 3.14 for π, and do not round your answer.

Explanation:

Step1: Find the radius of the candle

The diameter \(d = 6\) inches. The radius \(r=\frac{d}{2}\), so \(r = \frac{6}{2}=3\) inches.

Step2: Calculate the volume of one candle

The volume formula for a cylinder is \(V=\pi r^{2}h\). Given \(\pi = 3.14\), \(r = 3\) inches, and \(h=4\) inches.
Substitute the values: \(V=3.14\times3^{2}\times4\).
First, calculate \(3^{2}=9\). Then \(V = 3.14\times9\times4\).
\(3.14\times9 = 28.26\), and \(28.26\times4=113.04\) \(in^{3}\) (volume of one candle).

Step3: Calculate the volume of 140 candles

Multiply the volume of one candle by 140. So \(113.04\times140\).
\(113.04\times140=(100 + 13.04)\times140=100\times140+13.04\times140\).
\(100\times140 = 14000\), \(13.04\times140=(13 + 0.04)\times140=13\times140+0.04\times140\).
\(13\times140 = 1820\), \(0.04\times140 = 5.6\). Then \(13.04\times140=1820 + 5.6=1825.6\).
\(14000+1825.6 = 15825.6\) \(in^{3}\).

Answer:

\(15825.6\)