Question

a company makes wax candles in the shape of a solid sphere. suppose each candle has a diameter of 15 cm. if the company has a total of 70,650 cm³ of wax, how many candles can be made? use 3.14 for π, and do not round your answer.

Explanation:

Step1: Find the radius of the candle

The diameter \(d = 15\) cm. The radius \(r=\frac{d}{2}=\frac{15}{2}=7.5\) cm.

Step2: Calculate the volume of one spherical - shaped candle

The volume formula for a sphere is \(V=\frac{4}{3}\pi r^{3}\). Substitute \(r = 7.5\) cm and \(\pi=3.14\) into the formula:

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Step3: Calculate the number of candles

Let \(n\) be the number of candles. We know that the total volume of wax is \(V_{total}=70650\) cm³. Using the formula \(n=\frac{V_{total}}{V}\), substitute \(V_{total}=70650\) and \(V = 1766.25\)

$$n=\frac{70650}{1766.25}=40$$

Answer:

40