The labels of the y-axis of the graphs, and areas, and circumferences obtained based on the formula for the area and circumference of a circle are;
1. First part
First graph: The y-axis label is; area (m²)
Second graph: The y-axis label is; radius (m)
Third graph: The y-axis label is; Circumference (m)
2. Second part; The area of circle B is 4,500 in²
3. Third part; The circumference is 1 9/11 m
4. Fourth part; The circumference of Clare's circle is 75 cm
What is the equation for the area and circumference of a circle depending on its diameter, D?
A circle's area is equal to (D2)/4.
C = D is the circumference of a circle.
The radius of a circle is calculated as r = D/2.
C = D is the equation for the circumference of a circle.
A = D2/4 is the formula for calculating the area of a circle.
As a result, the radius and circumference equations are straight line equations, with the slope of the circumference equation () being greater than the slope of the radius equation (1/2).
Because the fluctuation of the area and diameter is A D2, the shape of the graph for the area is a cup-shaped parabola.
As a result, the labels on the y-axis of the graphs are;
The first graph's y-axis label is Area (m2).
Radius (m) is the label for the second graph's y-axis.
Circumference (m) is the third graph y-axis label.
Second section;
A circle's area is 500 in2.
The diameter of circle B equals three times the diameter of circle A.
We obtain; if D is the diameter of circle A.
Circle area A = 500 in2 = D2/4
D² = 4 × 500/π = 2000/π
Circle B has a diameter of 3D.
B's circle area = (3D)²/4 = π·9·D²/4
π·9·D²/4 = π × 9 × (2000/π)/4 = 4,500
Circle B has a surface area of 4,500 in2.
Part three;
Lin's bike traverses a distance of 100 meters.
The number of rotations of the wheels is 55.
Her wheel's circumference is thus 100 m 55 = 1 9/11 m.
Part four;
Priya's circle has a circumference of 25 cm.
Circle circumference Clare drew = 3 × The diameter of the circle Priya drew
The diameter of Priya's circle = 25/π
Priya's circle has a diameter of 25/
Clare's circle diameter = 3 25/ = 75/
Clare's circle circumference = 75/ = 75
Clare's circle has a circumference of 75 cm.