The diagram shows a square pyramid over a cube. What is the volume of the entire figure? CLEAR CHECK 324 cubic inches 594 cubic inches 810 cubic inches 972 cubic inches
The volume of a square pyramid is given by the formula V = (1/3) * B * h, where B is the area of the base and h is the height of the pyramid. The volume of a cube is given by the formula V = s^3, where s is the length of one side of the cube.
In this case, the base of the pyramid is a square with side length equal to the side length of the cube. Therefore, the area of the base of the pyramid is equal to the area of the cube.
Let's assume the side length of the cube (and also the base of the pyramid) is represented by x. The height of the pyramid is also equal to x.
The volume of the entire figure can be calculated as follows:
Volume of cube = x^3
Volume of pyramid = (1/3) * x^2 * x = (1/3) * x^3
Total volume = Volume of cube + Volume of pyramid
Total volume = x^3 + (1/3) * x^3
Total volume = (4/3) * x^3
Total volume = (4/3) * 729 cubic inches
Total volume = 972 cubic inches
Therefore, the volume of the entire figure is 972 cubic inches. The correct answer is 972 cubic inches.