cubes 1 and 2 are similar if the volume of cube 2 is 45 and the scale factor between sides of the two is 2:3 what is the volume of cube 1?
All cubes are similar
If the ratio of sides is r, the ratio of volumes is r^3.
So, if the sides of c2 are 2/3 those of c1, then volume is (2/3)^3 the volume of c1.
what is the answer to volume of cube B? How many cubes identical to cube A are needed to fill cube B?
To find the volume of cube 1, we need to apply the scale factor to cube 2 and then calculate the volume.
The scale factor between the sides of the two cubes is given as 2:3, which means that each side of cube 2 is two-thirds the length of the corresponding side of cube 1.
We can start by finding the length of each side of cube 2. Since the scale factor is 2:3, if we let the length of cube 2 be x, then the length of cube 1 would be (3/2) * x.
Given that the volume of cube 2 is 45, we can use the formula for the volume of a cube, which is V = length ^ 3.
So, for cube 2, we have 45 = x^3.
Now we can solve for x by taking the cube root of both sides: x = ∛45.
Next, we can find the length of cube 1 by multiplying the length of cube 2 by (3/2): (3/2) * ∛45.
Finally, we can calculate the volume of cube 1 by cubing the length of cube 1: (3/2 * ∛45) ^ 3.
So, the volume of cube 1 is (3/2 * ∛45) ^ 3.