Question

find the diagnol of a rectangle prism box that measures of 3x4x10cm round to nearest tenths

Answer 1

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**.