Math Problem Statement

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

Solution

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

  1. Volume to Edge Length Calculation: v=a    Volume of cube=a cubic yardsv = a \implies \text{Volume of cube} = a \text{ cubic yards} Since the volume VV of a cube is given by: V=s3V = s^3 where ss is the edge length in yards. Therefore: s3=a    s=a3 yardss^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 sinchess_{\text{inches}} is: sinches=a3×36 inchess_{\text{inches}} = \sqrt[3]{a} \times 36 \text{ inches}

Thus, the length of each edge of the cube in inches is a3×36\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.

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Math Problem Analysis

Mathematical Concepts

Geometry
Volume
Surface Area
Unit Conversion

Formulas

Volume of a cube: V = s^3
Surface area of a cube: A = 6s^2

Theorems

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Suitable Grade Level

High School