Answer:
Step-by-step explanation:
1). Let the circumference C and area A of the circle are proportional,
C ∝ A
C = kA
Here k = proportionality constant
k = [tex]\frac{C}{A}[/tex]
From the given table,
For C = 25 cm, A = 50 cm²
Then the value of k = [tex]\frac{25}{50}[/tex]
k = [tex]\frac{1}{2}[/tex]
For C = 50 cm, A = 201 cm²
k = [tex]\frac{50}{201}[/tex] ≈ [tex]\frac{1}{4}[/tex]
In both the cases proportionality constant is giving the different values.
Therefore, Circumference and Area of the circular objects are not proportional.
2). If A = [tex]\frac{1}{2}\times r\times C[/tex]
Then this equation will be true for all the values of r and C given in the table.
For r = 4 cm and C = 25 cm
A = [tex]\frac{1}{2}\times 4\times 25[/tex] = 50 cm²
For r = 8 cm and C = 50 cm
A = [tex]\frac{1}{2}\times 8\times 50[/tex]
A = 200 cm²
True for all values of 'r' and 'C'.
