What is the length of the longest rod that can be placed in a hollow cube of side 10 feet?

in this problem we are supposed to use Pathagorem Theorm.

diagonal^2=lenght^2 + width^2 + height^2

This formula applies to all rectangular solids.

To find the length of the longest rod that can be placed in a hollow cube of side 10 feet, we can use the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, if we consider the longest rod to be the hypotenuse of a right triangle, we can use the theorem to determine its length.

In a cube, the longest diagonal is the space diagonal, which can be found by connecting two opposite corners of the cube.

Let's label the sides of the cube as a, b, and c. In this case, all sides of the cube have a length of 10 feet.

To find the space diagonal, we can apply the Pythagorean theorem to the three-dimensional right triangle formed by the sides of the cube.

The formula for the length of the space diagonal (d) can be derived as follows:

d² = a² + b² + c²

Substituting the values with side lengths of 10 feet, we get:

d² = 10² + 10² + 10²
= 100 + 100 + 100
= 300

Taking the square root of both sides, we find:

d = √300
≈ 17.32 feet

Therefore, the length of the longest rod that can be placed in the hollow cube with a side length of 10 feet is approximately 17.32 feet.