Ratio of the areas of the circumcircle and incircle of a square
= [(Diagonal)²π] / [(Side)²π]

Correct Option: A

Ratio of the areas of the circumcircle and incircle of a square
= [(Diagonal)²π] / [(Side)²π]
= [(Side x √2)²] / (Side)² = 2/1 or 2 : 1

Increase in circumference of circle = 5%
∴ Increase in radius is also 5%.
Now, increase in area of circle = 2a + (a²/100) %

Correct Option: B

Increase in circumference of circle = 5%
∴ Increase in radius is also 5%.
Now, increase in area of circle = 2a + (a²/100) %
Where, a = increase in radius= 2 x 5 + (5 x 5)/100 % = 10.25%

Let original radius be r.
Then, according to the questions,
π (r + 1)² - πr² = 22

Correct Option: C

Let original radius be r.
Then, according to the questions,
π (r + 1)² - πr² = 22
⇒ π x [(r + 1)² - r²] = 22
⇒ (22/7) x (r + 1 + r ) x (r + 1 - r) = 22
⇒ 2r + 1 = 7
⇒ 2r = 6
∴ r = 6/2 = 3 cm

Length of to the rope = Radius of circle
According to the question,
πr² = 154

Correct Option: A

Length of to the rope = Radius of circle
According to the question,
πr² = 154
∴ r² = 154 x (7/22) = 7 x 7 = 49
∴ r = √49 = 7 m

The man takes 3600 s for 14.4 km
The man will take 88 s for
14.4 x (88/3600) = 352/1000 km = 352 m

Now, circumference of circular field = 352 m
⇒ 2πr = 352 m
2 x (22/7) x r = 352
⇒ r = 56 m

Therefore, area of the field = πr²

Correct Option: B

The man takes 3600 s for 14.4 km
The man will take 88 s for
14.4 x (88/3600) = 352/1000 km = 352 m

Now, circumference of circular field = 352 m
⇒ 2πr = 352 m
2 x (22/7) x r = 352
⇒ r = 56 m

Therefore, area of the field = πr²
= (22/7) x 56 x 56
= 8 x 22 x 56 m²
= 9856 sq m.