Question

I cant seem to figure out this answer. Can anyone help?

A company makes wax candles in the shape of a solid sphere. Suppose each candle has a diameter of 18 cm. If the company has a total of 152,604 cm³ of w
how many candles can be made?
Use 3.14 for x, and do not round your answer.

Answer 1

50 spherical candles can be made with 152,604 cm³ of wax.

Explanation:

Since the wax candles are in the shape of a solid sphere, we can calculate the volume of one candle by using the volume of a sphere formula.

`\boxed{\begin{minipage}{4 cm}\underline{Volume of a sphere}\\\\$V=(4)/(3) \pi r^3$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}`

The diameter of a sphere is twice its radius.

Therefore, if the diameter of the spherical candle is 18 cm, its radius is:

`\implies r=(d)/(2)=(18)/(2)=9\; \sf cm`

Substitute r = 9 and π = 3.14 into the formula to calculate the volume of one spherical candle.

`\begin{aligned}\implies \textsf{Volume of one candle}&=\sf (4)/(3) \cdot 3.14 \cdot (9\;cm)^3\\\\&=\sf (4)/(3) \cdot 3.14 \cdot 729\;cm^3\\\\&=\sf 3052.08\; \sf cm^3\end{aligned}`

Given the company has a total of 152,604 cm³ of wax, to calculate how many candles can be made, divide the total amount of available wax by the wax needed to make one candle.

`\begin{aligned}\textsf{Total number of candles}&=\sf (152604\; cm^3)/(3052.08 \;cm^3)\\\\&=\sf 50\end{aligned}`

Therefore, 50 spherical candles can be made with 152,604 cm³ of wax.