Find the length of the arc equal to 5/7 of the circumference of a circle whose radius is 8.4 cm.
A circle is a flat geometric figure whose points are equidistant from a given point, the center of the circle.
1) Find the circumference.
Let’s write down the formula for determining the circumference in terms of the radius:
l = 2πR,
where l is the circumference, R is the radius, π = 3.14.
Substituting the known values of the radius and constant π into the formula, we find the circumference, l:
l = 2 × 3.14 × 8.4 = 52.75 cm.
2) Find the arc length equal to 5/7 of the circumference.
The length of a circular arc is a fraction of the length of the circle itself.
Let’s figure out what a 5/7 circle is. 5/7 is a fraction.
A fraction is a number made up of one or more parts of one. The denominator of the fraction shows how many parts the unit is divided into, and the numerator shows how many such parts were taken.
It turns out that the circumference was conventionally divided into 7 parts and took 5 parts. We need to find these 5 parts. To find 5/7 of the circumference, you need to divide the circumference by 7 and multiply by 5, that is, multiply by the fraction 5/7:
52.75 × 5/7 = (52.75 × 5) / 7 = 37.68 cm.
Answer: The length of the arc, equal to 5/7 of the circumference, is 37.68 cm.