Q5) A man is cycling along the boundary of a square park at a speed of 10.8 Km/hr and completes one round in 6 minutes. Then the area of the park (in sq m) is 1) 78400 2) 72900 3) 27000 4) 65600
Perimeter of the park = Distance covered in 6 minutes = (10800/60)×6 = 1080 m Side of the park = 1080/4 = 270 m Area = 270 ^{2} = 72900 sq m.Hence, option 2. Q6) Find the area of a circle whose circumference is 88 m. 1) 616 m ^{2}2) 1232 m ^{2}3) 308 m ^{2}4) 154 m ^{2}
Let 'r' be the radius of a circle of circumference 88 m 2πr = 88 2×(22/7)×r = 88 On solving, r = 14 m Area of a circle = πr ^{2} = (22/7)×14×14 = 616 m^{2}Hence, option 1. Q7) Area of two circular fields is in the ratio 25:49. If the radius of the latter is 14 m, find the radius of the former? 1) 7 m 2) 5 m 3) 19.6 m 4) 10 m
If ratio of areas is 25:49, then ratio of radii is √25:√49 = 5:7 R/14 = 5/7 R = 10 m Hence, option 4. Q8) The percentage increase in the area of a rectangle, if each of its sides is increased by 30% is: 1) 30% 2) 45% 3) 69% 4) 60%
Let original length be L and original breadth be B Initial Area = L × B As length and breadth are increased by 30% so new length be 1.3L and new breadth be 1.3B Final Area = (1.3L)(1.3B) = 1.69 LB ∴ Percentage increase Change in Area = Final Area - Initial Area = 1.69LB - LB = 0.69LB ∴ Percentage increase = 69% Hence, option 3. |