Which of the following expressions correctly shows the relationship between the circumference and the area of a circle?
Cd=π
A=πr2
C=2πr
C2=4πA
C=2πr
Radius Circumference Area
5 cm 31.4 cm 78.5 cm2
This chart is correctly developed with the circumference and the area of a circle with a radius of 5 cm.
The formula for the circumference of a circle is C = 2πr, so with a radius of 5 cm, the circumference is:
C = 2π(5) = 31.4 cm
The formula for the area of a circle is A = πr^2, so with a radius of 5 cm, the area is:
A = π(5)^2 = 78.5 cm^2
Therefore, the chart with the correct values for the circumference and area of a circle with a radius of 5 cm is:
Radius Circumference Area
5 cm 31.4 cm 78.5 cm2
If C=12π, what is the area of the circle?
36π
24π
12π
144π
To find the area of a circle, we use the formula A = πr^2. We are not given the value of the radius, but we are given the value of the circumference, which is C = 2πr. We can use this information to solve for the radius, and then use that value to find the area.
C = 2πr
12π = 2πr
r = 6
Now we can find the area:
A = πr^2
A = π(6)^2
A = 36π
Therefore, the area of the circle is 36π. Answer: 36π.
Which chart is correctly developed with the circumference and the area of a circle with a radius of 5 cm?
Radius Circumference Area
5 cm 15.7 cm 19.63 cm2
Radius Circumference Area
5 cm 78.5 cm 31.4 cm2
Radius Circumference Area
5 cm 62.8 cm 314 cm2
Radius Circumference Area
5 cm 31.4 cm 78.5 cm2
Which formula is used to find the area of a circle when given the radius?
A=r2
A=r
A=d2
A=2r
The formula used to find the area of a circle when given the radius is:
A = πr^2
Therefore, the correct formula is A = r^2. Answer: A = r^2.
Which formula is used to find the circumference of a circle when the radius is given?
C=r
C=r2
C=2d
C=2r
The formula used to find the circumference of a circle when the radius is given is:
C = 2πr
Therefore, the correct formula is C = 2r. Answer: C = 2πr.
To determine the correct expression that shows the relationship between the circumference and the area of a circle, let's analyze each option:
1. Cd=π: This expression does not relate the circumference (C) to the area (A) of a circle. It simply states that "Cd" is equal to "π," which is not relevant to the question.
2. A=πr2: This expression establishes the relationship between the area (A) of a circle and its radius (r) squared, multiplied by the mathematical constant π. It does not involve the circumference (C) of the circle.
3. C=2πr: This expression correctly relates the circumference (C) of a circle to its radius (r) and the mathematical constant π. It states that the circumference is equal to two times π multiplied by the radius.
4. C2=4πA: This expression incorrectly relates the square of the circumference (C2) to the area (A) of a circle multiplied by 4π. It does not represent the relationship between the circumference and the area.
Therefore, the expression that correctly shows the relationship between the circumference (C) and the area (A) of a circle is C=2πr.