Q17) If radius of a circle is decreased by 20%, find the percentage change in area? 1) 36% 2) -44% 3) -20% 4) -36%
Let the initial radius be 1 unit. Initial area = π(1) ^{2} = π (radius = 1 unit)Radius of a circle is decreased by 20% ∴ New radius = 0.8 units Final area = π(0.8) ^{2} = 0.64πPercentage Change in Area Change in Area = Final Area - Initial Area = 0.64π - π = -0.36π Percentage Change in Area = -36% Hence, option 4. Q18) A bedsheet when washed, lost 22% of its length and 10% of its breadth. Find the percentage decrease in the area? 1) 32% 2) 24.2% 3) 29.8% 4) 17.5%
Let original length be L, original breadth be B. Initial_Area = LB Final_Area = (0.78L)(0.9B) = 0.702LB ∴ Percentage Change in Area Change in Area = Final Area - Initial Area = 0.702LB - LB = -0.298LB Percentage Change in Area = -29.8% -ve sign indicates decrease in area. Hence, option 3. Q19) The ratio between the perimeter and the length of the rectangle is 7:2. If the area of the rectangle is 192 sq.cm, then what is the breadth of the rectangle? 1) 16 cm 2) 12 cm 3) 20 cm 4) 15 cm
P/L = 7/2 2(L + B)/L = 7/2 4(L + B) = 7L 4B = 3L B = 3L/4 Area = L × B = 3L ^{2}/4 = 192L ^{2} = 256L = 16 Hence, option 1. |