A circle has a circumference of 110.6 mm. Find its diameter to the nearest tenth.
well, C = πd, so ...
C=#D
therefore, D=C/#
=110.6/(22/7)
=110.6×7/22
=35.19
=35.2mm
To find the diameter of a circle, we first need to know the formula for finding the circumference of a circle. The formula for the circumference (C) of a circle is given by:
C = 2πr
Where C is the circumference, π (pi) is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.
However, in this case, we are given the circumference (C) of the circle, not the radius (r). So we need to rearrange the formula to solve for the radius:
C = 2πr
Dividing both sides of the equation by 2π, we get:
r = C / (2π)
Now we can substitute the given circumference (C = 110.6 mm) into the equation to find the radius:
r = 110.6 mm / (2 × 3.14159)
r ≈ 17.6 mm
The radius of the circle is approximately 17.6 mm.
To find the diameter (d), we double the radius:
d = 2r
d ≈ 2 × 17.6 mm
d ≈ 35.2 mm
Therefore, to the nearest tenth, the diameter of the circle is approximately 35.2 mm.
To find the diameter of a circle given its circumference, we can use the following formula:
Circumference = π * Diameter
First, let's rearrange the formula to solve for the diameter:
Diameter = Circumference / π
Now, let's substitute the given value into the formula:
Diameter = 110.6 mm / π ≈ 35.2 mm (rounded to the nearest tenth)
Therefore, the diameter of the circle is approximately 35.2 mm to the nearest tenth.