a company makes wax candles in the shape of a solid sphere. suppose each candle has a diameter of 15 cm. if…
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 35,325 cm³ of wax, how many candles can be made? use 3.14 for π, and do not round your answer.
Answer
Explanation:
Step1: Calculate radius of sphere
Given diameter $d = 15$ cm, radius $r=\frac{d}{2}=\frac{15}{2}$ cm.
Step2: Find volume of one - sphere - shaped candle
The volume formula for a sphere is $V=\frac{4}{3}\pi r^{3}$. Substitute $r = \frac{15}{2}$ cm and $\pi=3.14$ into the formula: [ \begin{align*} V&=\frac{4}{3}\times3.14\times(\frac{15}{2})^{3}\ &=\frac{4}{3}\times3.14\times\frac{15^{3}}{2^{3}}\ &=\frac{4}{3}\times3.14\times\frac{3375}{8}\ &=3.14\times\frac{3375}{6}\ &=3.14\times562.5\ & = 1766.25\text{ cm}^3 \end{align*} ]
Step3: Calculate number of candles
Let $n$ be the number of candles. We know the total volume of wax is $35325$ cm³. Then $n=\frac{\text{Total volume of wax}}{\text{Volume of one candle}}$. Substitute the values: $n=\frac{35325}{1766.25}=20$.
Answer:
20