Question

a company makes wax candles in the shape of a cylinder. each candle has a diameter of 8 inches and a height of 3 inches. if the company used 7988.16 in³ of wax, how many candles did it make? use 3.14 for π, and do not round your answer.

Explanation:

Step1: Calculate the radius of the cylinder

The diameter \(d = 8\) inches. The radius \(r=\frac{d}{2}\), so \(r = \frac{8}{2}=4\) inches.

Step2: Calculate the volume of one candle (cylinder)

The volume formula for a cylinder is \(V=\pi r^{2}h\). Substitute \(\pi = 3.14\), \(r = 4\) inches, and \(h = 3\) inches. Then \(V=3.14\times4^{2}\times3\). First, calculate \(4^{2}=16\). Then \(V=3.14\times16\times3\). \(3.14\times16 = 50.24\), and \(50.24\times3=150.72\) \(in^{3}\).

Step3: Calculate the number of candles

The total wax volume is \(7988.16\) \(in^{3}\). The number of candles \(n=\frac{7988.16}{V}\). Substitute \(V = 150.72\). Then \(n=\frac{7988.16}{150.72}=53\).

Answer:

\(53\)