A bicycle has a 100 cm diameter wheel. If you ride on and around a circle with a 10 km diameter 12 times, how many revolutions does the wheel make?
find the circumference of the wheel.
Find the circumference of the circuit, multiply it by 12 , then divide by the circumference of the wheel
change everything to metres. Since you are in the metric system, this is very easy to do.
Well, I hope that bicycle's wheel doesn't get too dizzy! Now, let's do some math.
First, let's convert the 10 km diameter of the circle to cm. Since 1 km equals 100,000 cm, the 10 km diameter will be 1,000,000 cm.
Now, let's calculate the circumference of the circle. The formula for the circumference is π * diameter. Using the new diameter of 1,000,000 cm, we get a circumference of 3,141,593 cm.
Since the wheel of the bicycle has a diameter of 100 cm, we can calculate how many times it will go around the circle by dividing the circumference of the circle by the circumference of the wheel.
So, 3,141,593 cm divided by 100 cm equals 31,415.93 revolutions.
But wait, we can't have partial revolutions! So, we'll round it down to the nearest whole number.
Therefore, the bicycle's wheel will make 31,415 revolutions around the 10 km diameter circle. That's quite the wild ride!
To find out how many revolutions the wheel makes, we need to find the distance that the bicycle travels in terms of the circumference of its wheel.
1. First, let's calculate the circumference of the bicycle wheel using the formula:
Circumference = π × Diameter.
Given that the diameter of the wheel is 100 cm, the circumference of the wheel is:
Circumference = π × 100 cm.
2. Now, let's convert the circumference to kilometers, since the given circle has a diameter in kilometers:
Circumference (in km) = (Circumference / 1000) km.
3. Next, let's calculate the distance that the bicycle travels in terms of the circumference of its wheel for one complete revolution:
Distance per revolution = Circumference (in km).
4. Since the bicycle rides around a circle with a diameter of 10 km twelve times, we need to calculate the total distance traveled:
Total distance traveled = Distance per revolution × 12.
5. Finally, to find the number of revolutions the wheel makes, divide the total distance traveled by the distance per revolution:
Number of revolutions = Total distance traveled / Distance per revolution.
Let's calculate the number of revolutions the wheel makes step-by-step.
To find the number of revolutions the bicycle wheel makes, we need to calculate the circumference of the larger circle and then divide it by the circumference of the bicycle wheel.
First, let's find the circumference of the larger circle with a 10 km diameter. The diameter is given, so we can use the formula for the circumference of a circle, which is C = πd where C is the circumference and d is the diameter.
The diameter of the circle is 10 km, which is equivalent to 10,000 meters. Therefore:
C = πd = π * 10,000 meters.
Now we can calculate the circumference by multiplying π (approximately 3.1416) by the diameter:
C = 3.1416 * 10,000 meters.
Calculating this, we find that the circumference of the larger circle is approximately 31,416 meters.
Now, we need to find the circumference of the bicycle wheel. The diameter of the wheel is given as 100 cm, which is equivalent to 1 meter.
Using the same formula, C = πd, we can calculate the circumference of the bicycle wheel:
C = πd = π * 1 meter.
Calculating this, we find that the circumference of the bicycle wheel is approximately 3.1416 meters.
Finally, to find the number of revolutions, we divide the circumference of the larger circle by the circumference of the bicycle wheel:
Number of revolutions = Circumference of larger circle / Circumference of bicycle wheel.
Number of revolutions = 31,416 meters / 3.1416 meters.
Calculating this, we find that the bicycle wheel makes approximately 10,000 revolutions when riding on and around the larger circle 12 times.