A cube with a volume of 216 cm3 is cut down to a pyramid with the same size base and the same height as the original cube. What is the volume of the pyramid?
A.108 cm3
B.94 cm3
C.72 cm3
D.52 cm3
A cube with volume 216 has sides of length 6cm.
The volume of a pyramid is (1/3)*A*h (where A is the area of the base and h is the height of the pyramid).
Therefore, the volume is (1/3)*6*6*6 = 72 cm^3 (answer C).
To find the volume of the pyramid that was cut from the cube, we need to understand the relationship between the cube and the pyramid.
A cube is a three-dimensional shape with all sides being equal in length, and in this case, it has a volume of 216 cm^3. The volume of a cube is found by cubing the length of one side.
So, we can deduce that the length of each side of the cube is the cube root of 216 cm^3.
∛(216 cm^3) ≈ 6 cm
Since the pyramid has the same base as the cube, which is a square with side length 6 cm, the area of the base of the pyramid is 6 cm * 6 cm = 36 cm^2.
Now, we need to find the height of the pyramid. Since the height of the pyramid is the same as the height of the original cube, it is also 6 cm.
The formula for finding the volume of a pyramid is 1/3 * base area * height.
So, the volume of the pyramid = 1/3 * 36 cm^2 * 6 cm = 72 cm^3.
Therefore, the correct answer is C. 72 cm^3.