The volume of a cube is v cubic yards, and its surface area is a square feet. If v=a, what is the length in inches of each edge

To find the length of each edge of a cube when its volume is given as \( v \) cubic yards and its surface area is given as \( a \) square feet, we can follow these steps:

1. **Volume to Edge Length Calculation:**
   \[
   v = a \implies \text{Volume of cube} = a \text{ cubic yards}
   \]
   Since the volume \( V \) of a cube is given by:
   \[
   V = s^3
   \]
   where \( s \) is the edge length in yards. Therefore:
   \[
   s^3 = a \implies s = \sqrt[3]{a} \text{ yards}
   \]

2. **Convert Edge Length to Inches:**
   There are 36 inches in a yard. Therefore, the edge length in inches \( s_{\text{inches}} \) is:
   \[
   s_{\text{inches}} = \sqrt[3]{a} \times 36 \text{ inches}
   \]

Thus, the length of each edge of the cube in inches is \( \sqrt[3]{a} \times 36 \) inches.

Would you like further details or have any questions about this solution? Here are 5 related questions you might find interesting:

1. How do you convert between cubic yards and cubic feet?
2. What is the formula for the surface area of a cube?
3. How do you convert square feet to square yards?
4. If the volume of a cube is given in cubic meters, how would you convert it to cubic inches?
5. What are some real-life applications of calculating the volume and surface area of cubes?

**Tip:** Always remember to convert units properly when working with volumes and surface areas to ensure accuracy in your calculations.

Learn how to calculate the length of each edge of a cube when given its volume in cubic yards and surface area in square feet. This problem involves understanding cube geometry, unit conversion between yards and inches, and applying volume and surface area formulas. Suitable for high school students.

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