Question

question 2 (multiple choice worth 1 points) (06.01 lc) the volume of a pyramid that fits exactly inside a cube is 9 cubic feet. what is the volume of the cube? 3 cubic feet 6 cubic feet 18 cubic feet 27 cubic feet

Explanation:

Step1: Recall the volume relationship between a pyramid and a cube (or rectangular prism)

The volume of a pyramid is given by the formula \( V_{pyramid} = \frac{1}{3}Bh \), where \( B \) is the area of the base and \( h \) is the height. For a pyramid that fits exactly inside a cube, the base of the pyramid is the same as the base of the cube, and the height of the pyramid is equal to the edge length of the cube. Let the edge length of the cube be \( s \). Then the volume of the cube \( V_{cube} = s^3 \), and the base area of the pyramid \( B = s^2 \), and the height \( h = s \). So the volume of the pyramid \( V_{pyramid} = \frac{1}{3} \times s^2 \times s=\frac{1}{3}s^3 \). This shows that the volume of the pyramid is \( \frac{1}{3} \) of the volume of the cube.

Step2: Solve for the volume of the cube

We know that the volume of the pyramid \( V_{pyramid} = 9 \) cubic feet. From the relationship above, \( V_{pyramid}=\frac{1}{3}V_{cube} \). So we can solve for \( V_{cube} \) by rearranging the formula: \( V_{cube}=3\times V_{pyramid} \). Substituting \( V_{pyramid} = 9 \) into the formula, we get \( V_{cube}=3\times9 = 27 \) cubic feet.

Answer:

27 cubic feet (corresponding to the option "27 cubic feet")