Answer:
Explanation:
1). Let the circumference C and area A of the circle are proportional,
C ∝ A
C = kA
Here k = proportionality constant
k =
![(C)/(A)](https://img.qammunity.org/2022/formulas/mathematics/high-school/63ta5dl5z2m7iu93v2lq1xdu3nur0uxu7j.png)
From the given table,
For C = 25 cm, A = 50 cm²
Then the value of k =
k =
![(1)/(2)](https://img.qammunity.org/2022/formulas/mathematics/high-school/f0qcv9cek84ihznc3s7uf39dlk9xfru67q.png)
For C = 50 cm, A = 201 cm²
k =
≈
![(1)/(4)](https://img.qammunity.org/2022/formulas/mathematics/college/8sgkbqu3iaqhrj3ec3ravgp4pqwnwrhmb4.png)
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 =
![(1)/(2)* r* C](https://img.qammunity.org/2022/formulas/mathematics/high-school/f0gb1jvvh0mdtkk6a0g1utwut1r5pskqvk.png)
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 =
= 50 cm²
For r = 8 cm and C = 50 cm
A =
![(1)/(2)* 8* 50](https://img.qammunity.org/2022/formulas/mathematics/high-school/t09w20iacyu0d6c7le4uj7cxyv6azbhra1.png)
A = 200 cm²
True for all values of 'r' and 'C'.