Question

8.
An insect (it can fly) moves from one corner to
another comer of body diagonal of a cubical room of
side 10 m. The minimum distance travelled by the
insect is
​

Answer 1

Answer:

$\sqrt{1000}$

Answer 2

Answer:

$10\sqrt 3\ \rm m$.

Explanation:

According to the Pythagoras theorem,

For a right angled triangle,

$\rm (hypotenus)^2=(perpendicular) ^2+(base)^2$.

Using the Pythagoras theorem,

The length of the diagonal of a cube is given by

$\text{diagonal length} = \sqrt{l^2+l^2+l^2}$

where, $l$ is the length of the side of the cube.

Given, $l=10\ m$.

Therefore, the length of the diagonal of the room is given by

$\text{ diagonal}=\sqrt{10^2+10^2+10^2} = 10\sqrt 3\ \rm m.$

The minimum distance traveled by the insect from one corner to another opposite corner is the length of the diagonal.