Answer and Step-by-step explanation:
To find the volume of the new cube, we can use the relationship between the surface area and the volume of a cube.
1. Determine the length of each side of the original cube:
Let's assume that the length of each side of the original cube is "x".
2. Find the surface area of the original cube:
The surface area of a cube is given by 6 times the length of one side squared. Therefore, the surface area of the original cube is 6x^2.
3. Set up an equation based on the given surface area:
We are given that the surface area of the original cube is 96 square yards. So, we can write the equation as:
6x^2 = 96
4. Solve the equation for the length of each side:
Divide both sides of the equation by 6:
x^2 = 16
Take the square root of both sides:
x = 4
Therefore, the length of each side of the original cube is 4 yards.
5. Calculate the length of each side of the new cube:
Since the length of each side of the original cube is doubled, the length of each side of the new cube is 2 times the original length, which is 2 * 4 = 8 yards.
6. Find the volume of the new cube:
The volume of a cube is given by the length of one side cubed. So, the volume of the new cube is 8^3 = 512 cubic yards.
Therefore, the volume of the new cube is 512 cubic yards.