The circumference of a circle varies directly from its diameter. If the circumference of the circle having a diameter of 7cm is 7 cm, what is the circumferences of the circle whose diameter is 10cm? 18cm? 20cm?
a. Write a mathematical statement that relate two quantities involved in the problem
b. What is the constant of variation? Formulate the mathematical equation
c. Construct a table of values from the relation.
Please Help me. !
a. The mathematical statement that relates the circumference and diameter of a circle is:
Circumference = constant * Diameter
b. The constant of variation in this problem is the ratio between the circumference and the diameter of the circle. It can be calculated as:
constant of variation = Circumference / Diameter
Using the given information that the circumference of the circle with a diameter of 7 cm is 7 cm, we can calculate the constant of variation:
constant of variation = 7 cm / 7 cm = 1
Therefore, the mathematical equation is:
Circumference = 1 * Diameter
c. To construct a table of values from the relation, we can use the mathematical equation from above:
For a diameter of 10 cm:
Circumference = 1 * 10 cm = 10 cm
For a diameter of 18 cm:
Circumference = 1 * 18 cm = 18 cm
For a diameter of 20 cm:
Circumference = 1 * 20 cm = 20 cm
Table of values:
Diameter (cm) | Circumference (cm)
7 | 7
10 | 10
18 | 18
20 | 20
Therefore, the circumferences for the circles with diameters of 10 cm, 18 cm, and 20 cm are 10 cm, 18 cm, and 20 cm respectively.