The question is asking for the cubic feet inside the prism, which means it wants the volume.
The volume equation is: Volume= length x width x height
The issue is: the measurements of the prism are given to us in inches, while the problem asks for feet. We just need to convert each measurement, by dividing each by 12, since there are 12 inches per foot. 40 inches/12=3.33 feet 45 inches/12=3.75 feet 30 inches/12=2.5 feet
Now, we just have to plug in the numbers we found to solve for the volume. V=(3.33 feet)(3.75 feet)(2.5 feet) V=31.22 cubic feet
The volume of water in the vase is the difference of volume of cylinder and that of the marbles. Vcylinder = πr²h = π(6 in)²(12 in) = 432π in³ Vmarbles = 9(4πr³/3) = 9(4π(3 in)³/3) = 324 π in³ The difference of the volumes is 108π in³.
