Question

The diagram shows a 5 cm x 5 cm x 5 cm cube.

A
Calculate the length of the diagonal AB.
Give your answer correct to 1 decimal place.

Answer 1

AB = 5.7 cm

Explanation:

base diagonal = square root( 5^2 + 5^2 ) = 7.07 cm

AB = square root ( 7.07^2 + 5^2 ) = 5.7 cm

Answer 2

The length of the diagonal
`\( AB \)` of the cube is approximately
`\( 8.7 \) cm` when rounded to 1 decimal place.

To calculate the length of the diagonal
`\( AB \)` of the cube, we can use the space diagonal formula for a cube which is derived from the Pythagorean theorem in three dimensions. The formula for the space diagonal
`(\( d \))` of a cube with side length
`\( a \)` is:

`\[ d = √(a^2 + a^2 + a^2) \]`

Since the cube has sides of 5 cm, we plug that into the formula:

`\[ d = √(5^2 + 5^2 + 5^2) \]`

`\[ d = √(25 + 25 + 25) \]`

`\[ d = √(75) \]`

`\[ d \approx 8.7 \text{ cm} \]`

Thus, The answer is 8.7 cm.