The ratio of the volume of cube A to the volume of cube B is 64 to 27. Use this information to determine the ratio of the length of a side of Cube A to the length of a side of cube B.
the ratio of the volumes of two similar shapes is proportional to the cubes of their corresponding sides.
so ?^3/?^3 = 64/27
ratio of sides must be 4 : 3
To determine the ratio of the length of a side of Cube A to the length of a side of Cube B, we need to recognize the relationship between the volume and the length of the sides of the cubes.
The volume of a cube is determined by cubing the length of one side. Therefore, if the length of a side of Cube A is represented by "x," then the volume of Cube A is x^3. Similarly, if the length of a side of Cube B is represented by "y," then the volume of Cube B is y^3.
Given that the ratio of the volume of Cube A to the volume of Cube B is 64 to 27, we can express it algebraically as follows:
(x^3) / (y^3) = 64 / 27
To simplify the equation, we can take the cube root of both sides:
∛[(x^3) / (y^3)] = ∛(64 / 27)
Simplifying further:
(x / y) = ∛(64 / 27)
Now, we can evaluate the expression on the right side of the equation:
(x / y) = ∛(8/3)^3
The cube root of a number raised to the power of three is the number itself. Simplifying:
(x / y) = 8/3
Finally, we have the ratio of the length of a side of Cube A to the length of a side of Cube B:
The ratio is 8:3.