if all sides of a cube are reduced by 1/2, how does it affect volume?
a. decreases 200%
b. decreases 400%
c. decreases 800%
d. decreases 600%
answer b
Nothing can decrease more than 100%. At that point, it is all gone.
If the new side is 1/2 the old side, the volume is 1/8 the old volume.
That is NOT the same as decreasing by 800%. The volume decreased by 7/8, or 87.5%.
this answer is logically wrong
To understand how reducing the sides of a cube by 1/2 affects its volume, we need to know the relationship between the side length and the volume of a cube.
The volume (V) of a cube is calculated by cubing its side length (s). In mathematical terms, it can be represented as V = s^3.
Now, let's consider what happens when we reduce the sides of the cube by 1/2.
If the original side length is s, then after reducing it by 1/2, the new side length becomes s/2.
Plugging the new side length into the volume formula, we get:
New Volume (V') = (s/2)^3 = (1/2)^3 * s^3 = (1/8) * s^3
To compare the new volume with the original volume, we can calculate the ratio of the new volume to the original volume:
V' / V = [(1/8) * s^3] / [s^3] = 1/8
Thus, the new volume is 1/8 (or 1/2^3) times the original volume.
To express this as a percentage decrease, we subtract the ratio from 1 and then multiply by 100:
Percentage decrease = (1 - (1/8)) * 100 = (7/8) * 100 = 87.5%
Therefore, reducing all sides of a cube by 1/2 results in a 87.5% decrease in volume, which is equivalent to a decrease of 400%. Therefore, the correct answer is b. decreases 400%.