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
No
a. The mathematical statement that relates the two quantities involved in the problem is: "The circumference (C) of a circle is directly proportional to its diameter (d)."
b. The constant of variation is the constant that relates the circumference and the diameter of the circle. In this case, since the circumference varies directly with the diameter, the constant of variation is π, which is approximately 3.14. The mathematical equation can be formulated as:
C = π * d
c. We can construct a table of values using the given relation:
For a circle with diameter 7 cm:
C = π * 7 = 21.98 cm (approx.)
For a circle with diameter 10 cm:
C = π * 10 = 31.42 cm (approx.)
For a circle with diameter 18 cm:
C = π * 18 = 56.55 cm (approx.)
For a circle with diameter 20 cm:
C = π * 20 = 62.83 cm (approx.)
a. The mathematical statement that relates the circumference and diameter of a circle is:
Circumference = k * Diameter
b. In this case, since the circumference varies directly with the diameter, the constant of variation is k.
We can use the given information to find the value of k. The problem states that when the diameter is 7 cm, the circumference is also 7 cm.
So, we can substitute these values into the equation:
7 = k * 7
Simplifying the equation, we get:
k = 1
Therefore, the constant of variation is 1, and the mathematical equation is:
Circumference = Diameter
c. Now we can construct a table of values using the relation:
| Diameter (cm) | Circumference (cm) |
|---------------|--------------------|
| 7 | 7 |
| 10 | 10 |
| 18 | 18 |
| 20 | 20 |
In this table, as the diameter of the circle increases, the circumference remains the same, which is equal to the diameter.
C = πd
I don't see how the value for the circumference and diameter could both be 7. Do you have a typo?