a cube has an edge length of x cm write an equation for the volume v of the cube in term of x . if the length of each edge were doubled how would the volume change if the length were tripled how would volume
x³
i mean the equation would be v=x³
Yes, you are correct! The equation for the volume, V, of a cube with an edge length of x cm is V = x^3. This means that the volume of the cube is equal to the edge length cubed.
If the length of each edge were doubled, the new edge length would be 2x. To find the new volume, we substitute 2x for x in the equation: V = (2x)^3 = 8x^3. So, the volume would increase by a factor of 8.
If the length of each edge were tripled, the new edge length would be 3x. To find the new volume, we substitute 3x for x in the equation: V = (3x)^3 = 27x^3. So, the volume would increase by a factor of 27.
In summary:
- If the length is doubled, the volume is multiplied by 8 (2^3 = 8).
- If the length is tripled, the volume is multiplied by 27 (3^3 = 27).