The volume of the empty space in the box is about 521.24 cubic centimeters.
Practice makes perfect
We are asked to find the volume of the empty space in the following box with two cylindrical candles. Think of this as having a box with two objects, anything, inside and wanting to find how much empty space is still inside the box. In this case, the box is filled with two candles.
Since the two candles are identical, the volume of the empty space is the difference between the volume of the box and two times the volume of one candle.
\begin{gathered}
V_\text{empty}=\textcolor{darkorange}{V_\text{box}}-2\textcolor{darkviolet}{V_\text{candle}}
\end{gathered}
The box is in the shape of a rectangular prism with dimensions that are 18 by 9 by 15 centimeters. Its volume is the product of its dimensions.
\begin{gathered}
\textcolor{darkorange}{V_\text{box}}=18\cdot 9\cdot 15=\textcolor{darkorange}{2430}\,\text{cm}^3
\end{gathered}
Each candle is a cylinder with a radius of 4.5 centimeters and a height of 15 centimeters. Now we will find the volume of one candle using the formula for the volume of a cylinder.
