find the similarity ratio of a cube with volume 729 m^3 to a cube with volume 3,375 m^3?
3:5
To find the similarity ratio between two objects, we can compare their corresponding side lengths or volumes.
In this case, we are comparing the volume of two cubes. Let's denote the side length of the first cube as "x" and the side length of the second cube as "y".
The volume of a cube is given by the formula V = side length^3.
For the first cube with a volume of 729 m^3, we have:
729 = x^3
Solve for x by taking the cube root of both sides:
∛729 = ∛x^3
9 = x
So, the side length of the first cube is 9 meters.
For the second cube with a volume of 3,375 m^3, we have:
3,375 = y^3
Solve for y by taking the cube root of both sides:
∛3,375 = ∛y^3
15 = y
So, the side length of the second cube is 15 meters.
To find the similarity ratio, we take the ratio of the corresponding side lengths:
Ratio = x / y = 9 / 15
Simplify the ratio:
Ratio = 3 / 5
Therefore, the similarity ratio of the cube with a volume of 729 m^3 to the cube with a volume of 3,375 m^3 is 3:5.
volume of 2 similar objects is proportional to the cube of their sides
so small side^3/large side^3 = 729/3375
small side / large side = (729/3375)^(1/3) = 9/15 or 0.6