Question

The formula C=3.14d can be used to approximate the circumference of a circle given its diameter. Company A manufactures and sells a certain washer with an outside circumference of 10 centimeters. The company has decided that a washer whose actual circumference is in the interval 9.8≤C≤10.2 centimeters is acceptable. Use a compound inequality and find the corresponding interval for diameters of these washers.

Answer 1

A corresponding interval for diameters of these washers is 3.121 ≤ d ≤ 3.248.

In Mathematics and Geometry, the circumference of a circle can be determined by using the following mathematical equations:

C = πd or C = 2πr

Where:

C represents the circumference of a circle.

D represents the diameter of a circle.

r represents the radius of a circle.

By substituting the given parameters into the formula for the circumference of a circle, we have the following;

9.8 = 3.14d

d = 9.8/3.14

d = 3.1210

10.2 = 3.14d

d = 10.2/3.14

d = 3.2484

Therefore, a compound inequality and the corresponding interval for diameters of these washers is given by;

3.121 ≤ d ≤ 3.248

Check:

C = 3.14 × 3.222

C = 10.11708 (Within the actual circumference).