Answer:
Activity 1:-
1) Pi (π) is the ratio of circumference and the diameter of the circle which is 22/7. So
[tex]\frac{c}{d} =\pi = \frac{22}{7}[/tex]
[tex]=> c = \frac{22}{7} d[/tex] where circumference is directly proportional to diameter (d).
2) Area of a parallelogram = Altitude × Base
Base = 10 cm. So ,
[tex]A = 10a[/tex] where area (A) is directly proportional to altitude (a).
3) Let the fare of 1 unit distance be f
So, for distance d , total fare (F) will be [tex]F = fd[/tex] where total fare (F) is directly proportional to distance (d).
4) Let the distance be 'D' , speed be 's' & time be 't' .
We know that [tex]s = \frac{D}{t}[/tex] where speed (s) is directly proportional to distance (D) & inversely proportional to time (t).
5) We know that area of a square (A) = side² (s²)
[tex]=> A = s^{2}[/tex] where area(A) is directly proportional to side(s).
Activity 2:-
1) p is directly proportional to sum of u & w.
⇒ p ∝ u + w
⇒ p = k (u + w)
Putting the values of p , u & w
⇒ 14 = k(4 + 3)
⇒ 7k = 14
⇒ k = 14/7 = 2
2) r is directly proportional to square of t.
⇒ r ∝ t²
⇒ r = k × t²
Putting the values of r & t
⇒ 16 = k × 16²
⇒ k = 16² ÷ 16 = 16
3) y is directly proportional to cube root of x.
⇒ y ∝ ∛x
⇒ y = k × ∛x
Putting the values of x & y ,
⇒ 2 = k × ∛27
⇒ 3k = 2
⇒ k = 2/3
4) z is directly proportional to cube of d.
⇒ z ∝ d³
⇒ z = k × d³
Putting the values of d & z ,
⇒ 5 = k × 2³
⇒ 8k = 5
⇒ k = 5/8
5) Total Surface Area (SA) is directly proportional to square of the sides (s).
⇒ SA ∝ s²
⇒ SA = k × s²
Putting the values of SA & s ,
⇒ 96 = k × 4²
⇒ 16k = 96
⇒ k = 96/16 = 6
