Question

For each pair of quantities given below, check whether the fisrt is proportional to the second.for proportional quantities, calculate the constant of proportionality. a) perimeter and radius of circles b)Area and radius of circles​

Answer 1

Answer:

a)  Let the perimeter be 'p' and radius be 'r'

2. We know that p = 2πr

3. We can put whatever value we like for r on the right side of the above equation. So r is a variable

4. What ever value we give for r, that value will be multiplied by a constant 2π. So p will always be proportional to r

5. The constant of proportionality is p/r = 2π

b)   The two quantities are:

(i) Area of the circle

(ii) Radius of the circle

1. Let the area be 'a' and the radius be 'r'

2. We know that a = πr2 = π × r × r

3. We can put whatever value we like for r on the right side of the above equation. So r is a variable.

4. Whatever value we give for r, that value will be multiplied by a 'constant π' and the 'variable r'. That means, r is not multiplied by the same constant every time.  

5. So a and r are not proportional