To find the diagonal of a rectangular prism (box), you can use the formula:
\[ d = \sqrt{l^2 + w^2 + h^2} \]
where \( d \) is the diagonal, \( l \) is the length, \( w \) is the width, and \( h \) is the height of the prism.
For the given dimensions of the rectangular prism:
- Length (\( l \)) = 3 cm
- Width (\( w \)) = 4 cm
- Height (\( h \)) = 10 cm
Plug these values into the formula:
\[ d = \sqrt{3^2 + 4^2 + 10^2} \] \[ d = \sqrt{9 + 16 + 100} \] \[ d = \sqrt{125} \] \[ d \approx 11.180339887498949 \]
Now, rounding to the nearest tenth:
\[ d \approx 11.2 \text{ cm} \]
The diagonal of the rectangular prism is approximately 11.2 cm.