Question

A diagonal of a cube measures 15 cm and the length of an edge of the cube is V75 cm.
What is the length of the diagonal of a face of the cube? Round to the nearest tenth.

Answer 1

Answer:

the diagonal of a face of the cube = 12.2 (Rounded to the nearest tenth)

Step-by-step explanation:

$\text{diagonal of the cube} =\ \left( \text{edge} \right) \times \sqrt{3}$

                                $=\sqrt{75} \times \sqrt{3}$

                                $=\sqrt{225}$

                                $=15$

$\text{diagonal of the face} =\left( \text{edge} \right) \times \sqrt{2}$

         

                               $=\sqrt{75} \times \sqrt{2} \\\\=\sqrt{150} \\\\=12.247448713916$