An insect flies from the corner A to corner B of a cubic room in 4 second where A and B are diagonally apposite corners. The side of the room is 4 m. The speed of the insect is

Options

A. `sqrt3 ` m/sec
B. `2sqrt3` m/sec
C. `sqrt2` m/sec
D. `2 sqrt2` m/sec

Answer

To find the speed of the insect flying from corner A to corner B of a cubic room, we can follow these steps:

### Step 1: Identify the given values
- The side length of the cubic room (A) = 4 m
- Time taken to fly from A to B = 4 seconds

### Step 2: Calculate the diagonal distance (d) from corner A to corner B
The formula for the diagonal distance (d) of a cube is given by:
\[ d = \sqrt{3} \times A \]
Substituting the value of A:
\[ d = \sqrt{3} \times 4 \]
\[ d = 4\sqrt{3} \text{ meters} \]

### Step 3: Use the formula for speed
The formula for speed (v) is:
\[ v = \frac{\text{distance}}{\text{time}} \]
Substituting the values we have:
\[ v = \frac{4\sqrt{3}}{4} \]

### Step 4: Simplify the speed calculation
\[ v = \sqrt{3} \text{ meters per second} \]

### Final Answer
The speed of the insect is \( \sqrt{3} \) meters per second.

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