The volume of a square pyramid is equal to _____ times the volume of a cube where the bases are the same, but the square pyramid is half the height of the cube.
its is equal to 2 times the volume because the square pyramid is HALF the height of the cube.
Next time, read the question a little more carefully, because the answer is in the question.
but that's not a choice.
A. 1/6
B. 1/3
C. 3
D. 6
cube: v = Bh
pyramid: 1/3 B(h/2) = 1/6 Bh
So, (A)
let the base of the pyramid and the cube be x by x
let the height of the pyramid be h
then the height of the cube is 2h
volume of pyramid = (1/3)x^2 h = (2/3)h x^2
volume of cube = x^2 (2h) = 2h x^2
ratio of cube : pyramid
= 2hx^2 : (2/3hx^2
= 2: 2/3
= 6:2
= 3:1
so it is 3 times as much, which is choice C
messed up my typing
don't know why my 1/3 suddenly became 2/3
How does the volume of a rectangular prism change if the width is reduced to 2004-06-01-04-00_files/i0280000.jpg of its original size, the height is reduced to 2004-06-01-04-00_files/i0280001.jpg of its original size, and the length is reduced to 2004-06-01-04-00_files/i0280002.jpg of its original size?
To find the relationship between the volume of a square pyramid and the volume of a cube, we need to apply the formula for the volume of each shape.
The volume V of a square pyramid is given by the formula:
V = (1/3) * base area * height
The volume V' of a cube is given by the formula:
V' = side length * side length * side length
In this case, the base of the square pyramid and the base of the cube are the same, but the height of the square pyramid is half the height of the cube. Let's assume the side length of the cube is "s". Since the base of the square pyramid is a square, its side length will also be "s".
Therefore, the base area of the square pyramid is:
base area = side length * side length = s * s = s^2
Now, we can substitute the values into the volume formulas:
Volume of the square pyramid:
V = (1/3) * base area * height
= (1/3) * s^2 * (s/2)
= (1/3) * (s^2 * s/2)
= (1/3) * (s^3/2)
= s^3/6
Volume of the cube:
V' = side length * side length * side length
= s * s * s
= s^3
Comparing the two volumes, we see that the volume of the square pyramid is (1/6) times the volume of the cube when the bases are the same, but the square pyramid is half the height of the cube.
Therefore, the volume of the square pyramid is equal to (1/6) times the volume of the cube.