Space Diagonal and Box Properties

Anil Kumar explains how to calculate the space diagonal of a square-based cardboard box using the Pythagorean theorem. The process involves first finding the diagonal of the base and then using it to calculate the space diagonal. The video provides a step-by-step guide to solving the problem, resulting in a space diagonal length of approximately 12.8 cm.

What is the shape of the base of the cardboard box discussed in the video?

• Triangle

• Square

• Circle

• Rectangle

What is the length of each side of the base of the cardboard box?

• 12 cm

• 10 cm

• 8 cm

• 6 cm

What is the first step in finding the space diagonal of the box?

• Calculate the volume of the box

• Find the diagonal of the base

• Measure the height of the box

• Determine the surface area of the box

Which mathematical property is used to find the diagonal of the base?

• Pythagorean theorem

• Quadratic formula

• Law of Sines

• Law of Cosines

What is the length of the diagonal of the base of the box?

• 8√2 cm

• 14 cm

• 10 cm

• 12 cm

What is the height of the box used in the calculation?

• 4 cm

• 5 cm

• 6 cm

• 7 cm

How many times is the Pythagorean theorem applied in the process?

• Twice

• Once

• Three times

• Four times

What is the formula used to find the space diagonal after finding the base diagonal?

• AG² = AH² + GH²

• AG² = AH² × GH²

• AG² = AH² - GH²

• AG² = AH² ÷ GH²

What is the final calculated length of the space diagonal?

• 10.5 cm

• 11.8 cm

• 12.8 cm

• 13.5 cm

What is the approximate square root of 164 used in the final calculation?

• 13.1

• 12.8

• 13.4

• 12.5