the circumference of a circle is 120 millimeters. Which of the following inqualities is true for d, the diameter of the circle measured in millimeters? A. 10<d<20
B. 30<d<40
C. 50<d<60
D. 70<d<80
pi is about 3, so d is about 120/3 or 40.
But, pi is slightly larger than 3, so d is slightly smaller than 40.
(B)
To determine the correct inequality for the diameter of the circle, we need to use the formula for the circumference of a circle in terms of its diameter:
C = πd,
where C is the circumference and d is the diameter.
Given that the circumference is 120 millimeters:
120 = πd.
Now, let's solve for d by dividing both sides of the equation by π:
d = 120/π.
To approximate this value, we need to use an estimation for the value of π. Let's use the commonly used approximation, π ≈ 3.14:
d ≈ 120/3.14.
Calculating this, we find:
d ≈ 38.22.
Therefore, the value of d, the diameter of the circle, is approximately 38.22 millimeters.
Now let's evaluate the given inequalities to find which one is true:
A. 10 < d < 20
Substituting our value of d, we have:
10 < 38.22 < 20
This statement is false.
B. 30 < d < 40
Substituting the value of d, we have:
30 < 38.22 < 40
This statement is true.
C. 50 < d < 60
Substituting the value of d, we have:
50 < 38.22 < 60
This statement is false.
D. 70 < d < 80
Substituting the value of d, we have:
70 < 38.22 < 80
This statement is false.
Therefore, the correct inequality for d, the diameter of the circle, is:
B. 30 < d < 40.