0. A cube has an edge length of 5 cm . How many times greater will the volume be for a different cub with double the edge lengths? (show your work)

To determine how many times greater the volume of the second cube is compared to the first cube, follow these steps: 1. **Understand the Volume Formula for a Cube:** The volume \( V \) of a cube with edge length \( a \) is given by: \[ V = a^3 \] 2. **Calculate the Volume of the Original Cube:** - **Edge Length (\( a_1 \)):** 5 cm - **Volume (\( V_1 \)):** \[ V_1 = a_1^3 = 5^3 = 125 \text{ cm}^3 \] 3. **Determine the Edge Length of the Second Cube:** The second cube has double the edge length of the first cube. \[ a_2 = 2 \times a_1 = 2 \times 5 \text{ cm} = 10 \text{ cm} \] 4. **Calculate the Volume of the Second Cube:** - **Volume (\( V_2 \)):** \[ V_2 = a_2^3 = 10^3 = 1000 \text{ cm}^3 \] 5. **Find How Many Times Greater the Second Volume Is:** \[ \text{Ratio} = \frac{V_2}{V_1} = \frac{1000}{125} = 8 \] **Conclusion:** The volume of the second cube is **8 times greater** than the volume of the original cube.