Calculate Average Speed: 5 Laps on a 300-Meter Radius Circular Track

Question

Ivan does laps around a circular park which has a radius of 300 meters.

He completes 5 full circuits in 35 minutes.

What was Ivan's average speed?

300300300

Video Solution

Solution Steps

00:00 Calculate Gonen's speed
00:03 The given circle radius
00:06 We'll use the formula for calculating circle circumference
00:12 We'll substitute the radius value according to the given data and solve for the circumference
00:15 This is the circle's circumference
00:19 According to the data, Gonen circled it 5 times
00:25 This is the distance Gonen traveled
00:30 Speed equals distance divided by time
00:34 We'll substitute appropriate values and solve for speed
00:47 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we'll go through the following steps:

  • Calculate the circumference of the circular park.
  • Determine the total distance Ivan runs.
  • Find Ivan's average speed.

Step 1: Calculate the circumference of the circular park.
The formula for the circumference of a circle is C=2πr C = 2\pi r , where r r is the radius.
Given r=300 r = 300 meters, C=2π×300=600π C = 2\pi \times 300 = 600\pi meters.

Step 2: Determine the total distance Ivan runs.
Ivan completes 5 laps, so the total distance D D is given by:
D=5×600π=3000π D = 5 \times 600\pi = 3000\pi meters.

Step 3: Find Ivan's average speed.
The formula for average speed is v=total distancetotal time v = \frac{\text{total distance}}{\text{total time}} .
Total time = 35 minutes.
Average speed v=3000π35≈269.14 v = \frac{3000\pi}{35} \approx 269.14 meters per minute.

Therefore, Ivan's average speed is 269.14 269.14 meters per minute.

Answer

269.14 meter per minute

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Related Subjects

The Circumference of a Circle Elements of the circumference How is the radius calculated using its circumference? Perimeter

Question Types

Circumference: Using additional geometric shapes Circumference: Applying the formula