Question

the surface area of this cube is 7,266.24 square yards. what is the value of n?
n = square yards
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Explanation:

Step1: Recall the formula for the surface area of a cube.

A cube has 6 faces, and each face is a square with area \( n^2 \). So the surface area \( S \) of a cube is given by the formula \( S = 6n^2 \).

Step2: Substitute the given surface area into the formula.

We know that \( S = 7266.24 \) square yards. So we set up the equation:
\( 6n^2 = 7266.24 \)

Step3: Solve for \( n^2 \).

Divide both sides of the equation by 6:
\( n^2=\frac{7266.24}{6} \)
\( n^2 = 1211.04 \)

Step4: Solve for \( n \).

Take the square root of both sides. Since \( n \) represents the length of a side of a cube, we take the positive square root:
\( n=\sqrt{1211.04} \)
\( n = 34.8 \)

Answer:

\( 34.8 \)