Question

You are going on a field trip in a school bus. A special detector placed on one of the bus's tires counts the number of rotations completed by the tire during the journey. The tire's diameter is 111 meter, and it made 800080008000 rotations during the trip.
How far did the bus travel?

Answer 1

The distance is 278859895989589 m

Step-by-step explanation:

The diameter is the distance between two points on the circle that passes through the centre.

Radius is the distance from the centre of the circle to any point on the circle.

Given that diameter = 111 m

Radius = half of diameter = 111/2 m

To calculate the distance traveled by the bus, we need to find the circumference of the circle, then multiply with the number of rotations the bus has made.

This is because the when the bus tyre completes one rotation, the total circumference of the circle would be covered.

So, the circumference of the tyre with radius 111/2 is

$2 \pi r=2 \times \pi \times \frac{111}{2}=\pi \times 111=3.14 \times 111=348.54 m$

Now let us calculate the distance travelled by the school bus with the number of rotations given as 800080008000.

$\text { Distance }=800080008000 \times \text { circumference }$

$\text { Distance }=80008000800 \times 348.54$

$\therefore \text { Distance }=278859895989589 \ m$

Answer 2

27911591159.880 km is the distance traveled by the bus if the diameter of the tire is 111 meter and the rotations is 800080008000.

Given:

Diameter of the tire = 111 meter

Number of rotations = 800080008000

To find:

Distance traveled by the bus  = ?

Solution:

Given, the special detector placed on one of the bus's tires that counts the number of rotations completed by the tire during the journey calculated 800080008000 rotations.

The tire is circular with diameter (d) = 111 m  

We know, Distance traveled in 1 rotation of the circular tire = Circumference of the tire  

$\begin{array}{l}{=2 \pi r} \\ {=\pi 2 r} \\ {=\pi d} \\ {=\frac{22}{7} \times 111 m}\end{array}$

= 348.86 m

Distance traveled in 800080008000 rotation of the circular tire  $\begin{array}{l}{=800080008000 \times 348.86 m} \\ {=279115911590880 m} \\ {=279115911590.880 \mathrm{km}}\end{array}$

Hence, the bus traveled 27911591159.880 km.