if a polyhedron has a volume of 14 cm and is dilated by a factor of 1/5, what will be the volume of the dilated polyhedron? ROund your answer to the nearest thousandth if necessary
To find the volume of a dilated polyhedron, we need to multiply the original volume by the cube of the dilation factor.
1. Given that the polyhedron has a volume of 14 cm^3 and is dilated by a factor of 1/5.
2. Cube the dilation factor: (1/5)^3 = 1/125.
3. Multiply the original volume by the cube of the dilation factor: 14 cm^3 × 1/125 = 14/125 cm^3.
Rounding the answer to the nearest thousandth:
14/125 ≈ 0.112 cm^3.
Therefore, the volume of the dilated polyhedron is approximately 0.112 cm^3.
To find the volume of the dilated polyhedron, we need to understand the relationship between the original volume and the dilated factor.
When a polyhedron is dilated, the volume changes by the cube of the scale factor. In this case, the scale factor is 1/5.
To calculate the new volume, we multiply the original volume by the cube of the scale factor:
New Volume = Original Volume * (Scale Factor)^3
Substituting the given values:
New Volume = 14 cm * (1/5)^3
Calculating the cube of 1/5:
(1/5)^3 = 1/125
Now we can calculate the new volume:
New Volume = 14 cm * 1/125
Multiplying 14 and 1/125:
New Volume = 14/125
Rounding the answer to the nearest thousandth:
New Volume ≈ 0.112 cm³
Therefore, the volume of the dilated polyhedron is approximately 0.112 cm³.
as with all solids, the volume changes as the cube of the linear change.
So, if it dilated by a factor of 1/5, the volume changes by a factor of (1/5)^3 = 1/125.