How long is the edge of a cube whose volume is twice that of the cube below? Round to the nearest tenth.
The pic is of a cube with 8 as the length
2s^3 = (∛2 s)^3
That is, the sides will be ∛2 as big to produce a volume twice as big.
Remember that area grows as the square of the scale, and volume grows as the cube.
So, when scaling area, the length grows as √
when scaling volume, the length grows as ∛
Could you elaborate a little further than that? I am still a bit confused on how to find the answer.
come on, guy
if the side is now 8, then the side of a cube with twice the volume will be 8∛2
the side of a cube with 1/8 the volume would be 8∛(1/8) = 8/2 = 4
this is the same as saying that a cube with sides 1/2 as long has 1/8 the volume
To find the length of the edge of a cube whose volume is twice that of a given cube, we can follow these steps:
1. Determine the volume of the given cube. The formula to find the volume of a cube is: volume = edge^3.
In this case, the given cube has a volume of 8, so:
8 = edge^3
2. Solve for the edge length by taking the cube root of both sides of the equation.
∛8 = ∛(edge^3)
The cube root of 8 is 2, so:
2 = edge
Therefore, the edge length of the given cube is 2.
3. Find the volume of the cube whose volume is twice that of the given cube.
Since the volume of the given cube is 8, the desired cube will have a volume of 2 * 8 = 16.
4. Calculate the length of the edge for the desired cube.
Using the formula for the volume of a cube: volume = edge^3
We know that the volume is 16, so:
16 = edge^3
Solve for the edge length by taking the cube root of both sides of the equation.
∛16 = ∛(edge^3)
The cube root of 16 is approximately 2.52.
5. Round the edge length to the nearest tenth.
Rounding 2.52 to the nearest tenth gives us 2.5.
Therefore, the length of the edge of the desired cube is approximately 2.5 units.