Q1) Find the area of the sector of a circle whose radius is 14 cm and angle of the sector is 45 degrees. 1) 77 cm ^{2}2) 38.5 cm ^{2}3) 19.25 cm ^{2}4) 154 cm ^{2}Area of sector of radius 14 cm and 45 degrees as the central angle = (22/7)×14 ^{2}×(45/360) = 77 cm^{2}Hence, option 1. Q2) Area of a rectangle is 144 cm ^{2}. Its breadth is 9 cm. Find its length.1) 14 cm 2) 12 cm 3) 16 cm 4) 18 cm Let L be the length of the rectangle. ATQ, 9L = 144 L = 16 cm Hence, option 3. Q3) Ratio of length and perimeter of a rectangular plot is 2:5. What is the ratio of length and breadth of the plot? 1) 4:1 2) 3:1 3) 2:1 4) 3:2
As, the ratio of length and perimeter of a rectangular plot is 2:5 So, let us suppose that length is 2 units and Perimeter is 5 units Perimeter of a rectangle = 2(L + B) ∴ 5 = 2(2 + b) On solving, b = 1/2 Ratio of length and breadth of the plot = 2/(1/2)=4 Hence, option 1. Q4) If radius of a circle is increased by 20%, find the percentage change in area? 1) 40% 2) 20% 3) 44% 4) 22%
Let the initial radius be 1 unit. Initial area = π(1) ^{2} = π (radius = 1 unit)Radius of a circle is increased by 20% ∴ New radius = 1.2 units Final area = π(1.2) ^{2} = 1.44πPercentage Change in Area Change in Area = Final Area - Initial Area = 1.44π - π = 0.44π Percentage Change in Area Hence, option 3. |