To find the volume of the cube that contains a pyramid with a volume of 9 cubic feet, we need to use the relationship between the volumes of a cube and the pyramid that fits exactly inside it.
The formula for the volume of a pyramid is given by:
[tex]\[ \text{Volume of the pyramid} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]
In the case of a pyramid that fits exactly inside a cube, the base area and height of the pyramid are those of the cube. Hence, the relationship between the volume of the pyramid and the volume of the cube is:
[tex]\[ \text{Volume of the pyramid} = \frac{1}{3} \times \text{Volume of the cube} \][/tex]
Given that the volume of the pyramid is 9 cubic feet, we can set up the equation:
[tex]\[ 9 = \frac{1}{3} \times \text{Volume of the cube} \][/tex]
To find the volume of the cube, we can multiply both sides of the equation by 3:
[tex]\[ 9 \times 3 = \text{Volume of the cube} \][/tex]
[tex]\[ 27 = \text{Volume of the cube} \][/tex]
Therefore, the volume of the cube is 27 cubic feet.
So, the correct answer is:
O 27 cubic feet
