Question
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)
Ask by Pope Mcdonald. in Canada
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The volume of the second cube is 8 times greater than the original cube.
Solution
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.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To find the volume of a cube, you use the formula \( V = s^3 \), where \( s \) is the edge length. For the first cube with an edge length of 5 cm: \[ V_1 = 5^3 = 125 \text{ cm}^3 \] For the second cube with double the edge length (10 cm): \[ V_2 = 10^3 = 1000 \text{ cm}^3 \] Now, to find how many times greater the volume of the second cube is than the first cube: \[ \text{Times greater} = \frac{V_2}{V_1} = \frac{1000}{125} = 8 \] So, the volume of the second cube is 8 times greater than the first cube.
