Question

The diagram shows a square pyramid completely contained inside a cube. The apex of thepyramid touches the top of the cube.181818Find the volume of the empty space in the cube.cubic unitsBlank 1:

Answer 1

To find the volume of the empty space, we need to find the volume of the cube and the pyramid and then find the difference between both values.

VOLUME OF CUBE:

The volume of a cube is calculated as

$V=l^3$

The length of the cube is 18. Therefore, the volume is given to be

$\begin{gathered} V=18^3 \\ V=5832\text{ cubic units} \end{gathered}$

VOLUME OF PYRAMID:

The formula to calculate the volume is

$V=\frac{1}{3}ah$

Where

$\begin{gathered} a=\text{ Base area} \\ h=\text{ Height} \end{gathered}$

Since the base is an 18 unit square, and the height of the pyramid is 18 units as well, we can calculate the volume to be

$\begin{gathered} V=\frac{1}{3}\times18^2\times18 \\ V=1944\text{ cubic units} \end{gathered}$

VOLUME OF THE EMPTY SPACE:

The volume of the empty space can be calculated by subtracting the volumes of the cube and pyramid:

$\begin{gathered} V=5832-1944 \\ V=3888\text{ cubic units} \end{gathered}$