A fish starts from a point on the edge of a circular pond, swims 600 meters due south to reach another point on the edge, turns west seims 800 mts to reach another point on the edge . The circum ference of the pond in meters is

Options

A. ` 200 pi`
B. ` 100 pi`
C. `500 pi`
D. `1000 pi`

Answer

To solve the problem, we need to find the circumference of a circular pond given the distances the fish swims. Let's break down the steps:

### Step 1: Understand the Problem
The fish swims 600 meters south and then 800 meters west. We need to visualize this as a right triangle where:
- One leg (southward distance) is 600 meters.
- The other leg (westward distance) is 800 meters.

### Step 2: Identify the Right Triangle
Let’s denote the points as follows:
- Point R: Starting point on the edge of the pond.
- Point P: Point reached after swimming south (600 meters).
- Point Q: Point reached after swimming west (800 meters).

The triangle formed is triangle RQP, where:
- RP = 600 meters (south)
- PQ = 800 meters (west)

### Step 3: Use the Pythagorean Theorem
Since triangle RQP is a right triangle, we can use the Pythagorean theorem to find the hypotenuse (RQ):
\[ RQ^2 = RP^2 + PQ^2 \]
Substituting the values:
\[ RQ^2 = 600^2 + 800^2 \]

### Step 4: Calculate the Squares
Calculate \(600^2\) and \(800^2\):
\[ 600^2 = 360000 \]
\[ 800^2 = 640000 \]

### Step 5: Add the Squares
Now, add these two results:
\[ RQ^2 = 360000 + 640000 = 1000000 \]

### Step 6: Find RQ
Take the square root to find RQ:
\[ RQ = \sqrt{1000000} = 1000 \text{ meters} \]

### Step 7: Determine the Radius
Since RQ is the diameter of the pond, the radius (r) is half of the diameter:
\[ r = \frac{RQ}{2} = \frac{1000}{2} = 500 \text{ meters} \]

### Step 8: Calculate the Circumference
The formula for the circumference (C) of a circle is:
\[ C = 2\pi r \]
Substituting the radius:
\[ C = 2 \pi (500) = 1000\pi \text{ meters} \]

### Final Answer
The circumference of the pond is \(1000\pi\) meters.

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