# Determine the length of an edge of a cube, if the surface area is 186 square inches. Find how many inches long is one of its edges.

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Expert Answers

justaguide | Certified Educator

The surface are of a cube with side s is given by the expression 6*s^2.

Here we have the surface area as 186 square inches

6*s^2 = 186

s^2 = 31

=> s = sqrt 31

=> 5.5677 (approximately)

**The side of the cube has a length 5.5677 inches.**

Student Comments

giorgiana1976 | Student

The number of like faces of the cube is 6.

We'll note the length of the side of the cube as a.

The area of a face is:

A = a^2

Since there are 6 faces, we'll get the total area:

S = 6a^2

186 = 6a^2

We'll divide by 6:

a^2 = 31

a = sqrt 31

**a = 5.567 inches**

We'll validate just the positive value for the length.