A wheel covers a distance of 4312 meters after 98 cycles. Using 22 over seven in place of 𝜋, find the wheel’s diameter.
The first thing that we need to do is to find the distance that’s been covered during one cycle. And we can do this by dividing the total distance by the number of cycles. So we divide 4312 by 98. And popping that into a calculator will give us a distance of 44 meters. The mathematical word that we use for the distance around the edge of a circle is the circumference. And since we know that the wheel has covered 44 meters in one cycle, then we can say that the circumference is 44 meters.
To find the diameter, we can use the formula circumference equals 𝜋 times diameter. And we remember that the diameter of a circle is a line that passes from one side to the other through the center. It’s also equal to twice the radius. So we can substitute in our values for the circumference. And remembering that we can use 22 over seven for 𝜋. This will give us 44 equals 22 over seven times the diameter.
In order to get the diameter by itself, we need to divide both sides for our equation by 22 over seven. This will give us 44 divided by 22 over seven equals the diameter. Annoyed to divide by this fraction, 22 over seven, we changed the division to a multiplication and flipped the numerator and denominator. Giving us a calculation 44 times seven over 22 for our diameter. We can simplify this calculation if we noticed that 44 has two lots of 22 in it. Which leaves us with the calculation of two times seven for our diameter.
Therefore, the answer for the diameter is 14 meters.