Calculating the Diagonal Length of a Cube

This lesson focuses on calculating the diagonal length of a cube. It begins by defining the problem and setting up the variables, followed by deriving the formula for the diagonal using the Pythagorean theorem. The lesson then provides a step-by-step calculation of the diagonal length, using a cube with a side length of nine inches as an example. The exact answer is given as nine times the square root of three inches, with a decimal approximation of 15.6 inches. The lesson concludes by summarizing the process and ensuring the viewer understands how to calculate the diagonal length of a cube given its side length.

What is the main focus of this lesson?

• Calculating the perimeter of a cube

• Calculating the surface area of a cube

• Calculating the diagonal length of a cube

• Calculating the volume of a cube

What is the side length of the cube used in this example?

• Nine inches

• Eight inches

• Seven inches

• Six inches

Which two points are used to calculate the diagonal of the cube?

• Points A and B

• Points E and F

• Points A and G

• Points C and D

What is the first step in deriving the formula for the diagonal length?

• Calculating the surface area of the cube

• Calculating the perimeter of the cube

• Calculating the volume of the cube

• Calculating the distance between two adjacent vertices

What is the value of l squared in terms of x?

• 4x squared

• 3x squared

• 2x squared

• x squared

What theorem is used to find the diagonal length of the cube?

• Pythagorean theorem

• Binomial theorem

• Fundamental theorem of calculus

• Remainder theorem

What is the formula for the diagonal length of a cube?

• Square root of two times x

• Square root of three times x

• Square root of five times x

• Square root of four times x

What is the exact diagonal length of the cube with side length nine inches?

• Nine square root five inches

• Nine square root four inches

• Nine square root three inches

• Nine square root two inches

What is the approximate decimal value of the diagonal length?

• 17.6 inches

• 14.6 inches

• 15.6 inches

• 16.6 inches

What is the final step in calculating the diagonal length of a cube?

• Taking the square root of the calculated value

• Multiplying the side length by three

• Taking the cube root of the calculated value

• Multiplying the side length by two